YouTube team keep it clean. What's going on? It's engraving here with another video and this is a very interesting Question from subscribers Shout out to my guy Michael Blackman. He said him and his boys win a roasting session and They were trying to think who are the worst players to ever play for the Ravens who are the worst players in the Ravens franchise history That's a really good question. That's a really funny question. That's a really good question But I want y'all helping answer in this too, but before we get into this Let me introduce myself me. I'm engraving viz. It's my YouTube channel engraving viz and I'm a Ravens fan But on here we just talk football period So make sure you subscribe to the channel turn your notifications on and leave a like on the video Click the thumbs up button You can follow on Twitter Instagram and Snapchat all three are engraving vids and most importantly follow on Twitter because YouTube Even if you subscribe sometimes the notifications won't work turn your notifications on anyway But sometimes YouTube be just doing YouTube stuff We got to find ways to work around it But anyway, who is the worst who are the worst players in Ravens franchise history now really quick I did mention that this is an NFL question from subscriber. Um, I For anybody that has sent me a question from subscriber I Actually don't have any videos left that up that up that I haven't put out for questions from subscribers So what that means is that Once you see me reply to your Instagram DM or snapchat DM or Twitter DM with your NFL question from subscriber That means you'll probably see it whether it be that same day or the very next day Because I'm all caught up on all of them on all of them. So Just know that so anyway Worst players in Ravens franchise history no, but I'm in definitely not Where's where's players in Ravens franchise history the worst it's a tough question Make sure I'll leave a like on the video. How are you got all these people in here?  We asked who's the worst player in Ravens franchise history, man. Who is that? hmm Matt Elam could be on the list um What's up, Kai? What's up DJ Rainville? um Could Anthony right? Oh, um, oh, what's the Cory ivy? Cory ivy would be on the list for me Cory. I know definitely not cowboy. No, no, no, no um Cory ivy frank walker. He could be on the list frank walker um No, not not lee evans um A difference between most hated and the worst a big difference right there Um, Troy Smith was a quarterback. I wouldn't say him. Um But the worst players meaning they just they sucked. They were they were terrible. They sucked Elvis girl Elvis girl, I mean him and Trin Dillfield they were just there to they were just there as roster spots I feel like them Um, Sergio can't well Sergio kindle now. He never got to play so I couldn't really call him the worst He fell down the steps and that was it. Oh sure. He's right. Okay. There we go. Sure. He's right. That's one of them Wow, I I forgot about it. Wow. I did mention frank walker to rel. So appreciate that I did mention him. Sure. He's right. It's a really good one though. Patrick Johnson the wide receiver um I can't say he was terrible, but I can't say as good. He just didn't do anything He didn't do anything travis taylor um Yeah, he just he never worked out No, wrong. No, Sean O'Connor. No, that's false. He said carry. Williams was the definition of garbage That couldn't be further from false than I mean, no, that's false. That's false That is so false um Ray Lewis we got in Ray Lewis. No, he said he's just playing though um But shot no, I couldn't put the shot on that list. No Even though I'm rooting for him, but now he he's definitely not one of the worst players in Ravens franchise history Um, he got beat all the time. No, no, he even got interception and all Well, carry. Williams reminds me of Brandon card man People don't appreciate what they what what those guys did for the Ravens and they were definitely Um, they were solid. They weren't the best in the world, but they were solid They were taller guys. Um, they weren't the fastest, but they could get the job done Oh match up. Wow. Match up. Hmm Would I put him at the top of the list? No, but Yeah, match up. Hmm match up Okay, so yeah, Sergio kind of because he what did he play like Didn't he play in a preseason for us one time? I think I don't even remember what he did But yeah, he obviously ain't work out. No Kyle baller. We can't put him on there. Um, there's Matt Elam Um, so I think Matt Elam is definitely on there. Frank walk is definitely on there. Cory Ivy is definitely on there. Cherise Wright is definitely on there Cherise Wright Just I wish he would have played every game like he played in that Buffalo Bills game for us that game. He was a beast Other than that, he was just oh Kendrick Lewis How could I almost forget him Kendrick Lewis Kendrick Lewis he uh He makes me sick to my stomach, man You said I I did see you put over early. You think blindside was one of the worst. No, man Not blindside. What's up, CJ Vizz? um No, Kendrick Lewis though Kendrick Lewis for sure opposite Derek Mason. Leon, who you talking about? Oh, who's number 89? Oh, you talking about Mark Clayton? Mark Clayton No Not mark Clayton. No, he was he didn't work out He wasn't one of the worst, but he just didn't work out Billy Cundiff. No because Billy Cundiff He was he was killing it for a minute He was doing it actually pretty good for a minute Then he just I don't know where he just fell off. So I definitely wouldn't think he he was not one of the worst One of the most hated. Okay, but not one of the worst. It's a difference We're gonna do a video on some of the most hated too. Um, oh chairman Macklin, okay Yeah, after last season. Yeah um Michael Campanero was the seventh rounder. Where this comes from Where Michael Campanero comes from? Oh still seven folks at Michael camp. I honestly can't remember him doing anything other than the permanent term for sure Whoa, no, Michael Campanero. He definitely not one of the worst. He's one of the most injury prone, but definitely not one of the worst um He what what was Mike? He was the seventh rounder. I thought he's like a fifth or sixth or whatever But either way, um, he was just injury prone. That's what Michael can't Michael Campanero was Terrence Cody Um That's Cody, uh I guess Yeah, he didn't really do much. He was just there man. He just his big body. That's just there man. What's up, mr. Male Uh, what do you think?  He was ready for that, man Denial Ella be no, no, that's that's foolish demon. That's a foolish comment then Denial Ella be no He's definitely not one of these these solid man And man, he came in for Ray Lewis and did his thing Whoa, hold up. What are we doing? Hey, man? Yo, man Again, I don't know why y'all take it out on me. I see everybody comment I see everybody comments up and down, but y'all are not clicking the thumbs up button Click the thumbs up button. Just leave a like on the video Y'all typing these comments these short comments long comments It takes longer to type it takes longer to think of a comment to type it and to press enter Then it takes to click the thumbs up button. Come on, man. What's up? What's up? I don't know what the beef is with me. I don't think I did nothing to nobody man geez Sam said Matt Elam Yeah, we can go with Matt Elam for one Michael always so hyped up by the movie that is true. That is true Chris. That is that is very true That is very true. Um And he was he was captain false start. He I don't think he was one of the worst though He definitely got a lot of false thoughts though. He got a ring. Yeah, he got a ring with Baltimore and Philly So shout out to denil eleby man The real worst players are guys we don't know the names of Well, no, I would say those guys just the guys that we don't know the names of I would say those guys just didn't make them up. They just didn't do anything But if somebody is worse for them to be considered one of the worst in my my opinion and everybody else You feel free to share but to disagree or agree whatever Um, my opinion of somebody being one of the worst players is somebody that actually got a chance to do their thing Over and over and over and over again, and they just continue to suck. They continue to bring the team down They continue to just be a liability But alex louis, hold up. I think some of y'all are trolling with some of these responses, man some of Eugene Monroe No he Did they get Eugene Monroe? He just he didn't I don't think he was one of the worst but he just didn't live up to What we thought he was gonna live up to he didn't he didn't play like Jacksonville when he came to us Jeremy Zuda see Jeremy Zuda the first year. Oh, Jeremy Zuda was doing this thing man second year. He just fell off I don't know where it came from. I don't know what happened. He just fell off. Um He wasn't worth it. Yeah, he didn't end up being worth it He didn't end up being worth it. Um, because what we give up like a third and a fourth Or I forgot what we gave up for him, but it obviously didn't work out in Anthony Wright cow bowler. No, Anthony Wright. You can put him up there. Um Uh, disney punch said ed hardware or the linebacker. He played for the falcons too I don't know one of the worst And Harry apel said it is so then it is really it's billy cundiff I billy cundiff was See if to be one of the worst, okay, again my opinion I Other people may feel otherwise But my opinion for somebody to really be one of the worst players they I feel like you will have to have sucked the whole time You played there should be no good moments. There should be no great moments There should be no glory moments for your entire career. Why are you on the ravens?  You sucked. That's not the case of billy cundiff He like I said, he was killing the years before that He was killing it man. He was doing this thing. He saved me. You say uh ryan mallet Um ryan mallet did beat the stillers in that game.   Oh shocky brawl Wow shocky brown. Yes. We can I think we can put him on there too Austin how it now definitely not Austin how it he said bowler was worse than you think how bowler was worse than mallet The guy that beat the green bay packers like it's through four touchdowns on the packers with breath fall Um, no, I don't know. Uh cow bowler. Um, I don't know James Hurst. Oh the famous uh flacco acl They did pay him 18.5 mil man Do remember ethan brooks ethan brooks. Ooh No, I don't I can't say that I do ethan brooks No, I don't remember him. No Yeah, I did say kindrick louis harry. So kindrick louis definitely for sure kindrick louis all day every day And on my list my personal list He is right there. He is right there. He is right there frank walk I did put him on there too. Y'all hear about the new player ravens linebacker chris scanlin.  Uh, he came on. I mean, he was only with us for a year He came on he caught a pass like in a second game. Um, then he like got hurt. That's what it was. He got hurt Then that's thank thank goodness for lee evans though. Um, because if not for lee evans Then there may be no torey smith Reason I say that Hold on carter because I know you're naked and then you trying to come in here. You can't be on the video And you ain't even got a diaper on so no um lee evans uh, he he came in and Then lee evans got hurt lee evans got hurt And then in came torey smith and then the rest was history as We all know So shout out to him. Thank you lee Um, so yeah, we uh, we gotta appreciate lee evans even though people hate them and they got their reasons for hating them Even though he didn't drop the pass He did not drop the pass sterling shepherd or whatever sterling's last name was Uh, I forgot what his name was sterling something sterling more whatever his name was he stripped that out He took it away from him Lee evans all he had to do was hold on but sterling took it away from him But hey, that's fine leon. That's what it's about Everybody's not gonna agree with what I say. That's fine. I appreciate you coming through How do you feel about it leon? Because I want to hear oh tanning dogs. Whoa Tanning dogs jacoby jones definitely not come on man. I know you're playing with that one every kicker after stover and before Tucker no really kind of really kind of used to be killing it for a while market smith that was a receiver, right? How to carry williams a how to carry will We're How did carry williams and ace of jackson? Ace of jackson Cornerback wise. Yes return wise. No, he was a nice returner, but then cornerback why he couldn't cover me Haruki Nakamura the safety wow Shout out to shinsuke Nakamura. Maybe they brothers as wow Lacan williams now he um He just it wasn't that he sucked. He just never got a chance. He just never caught on Troy smith now. Oh Arthur brown. Who that's a good one. That's a good one. That's a recent one too Arthur brown matt elam both in the same draft, right? I think Lee evans real good and buffalo ravens garbage. Oh you talking about that Oh, no, okay. That's wait. That's that's what you disagreed with I this the video this video is called the worst Players to play for the ravens and ravens franchise history So meaning when they came to the ravens when they played for the ravens their time period playing for the ravens That's when they sucked Not i'm not talking about prior to the ravens or post the ravens I'm talking about while they were on the ravens so Lee evans while he was on the ravens. That's what I say. Yeah, he I understand understand that one jaylon hill. What how can jaylon hill? I know some of y'all trollin man. Y'all are trolling big time tonight. Um, Yo, james Harrison. Jeez. Well, yeah I guess they figured that he sucked while he was on the ravens and then they say, you know what? Bye He went to stillers and he killed us for years But no, I pierced no he's not on that list. No What's up polo Show potential free season but was nothing in regular season was injured all season long. Who you talking about drew?  Well, no, he wasn't injured all season long. He just ain't getting the game that much Jaylin hill ain't getting the game that much because we had all these other cornerbacks Jaylin hill was just on like special teams and stuff and he got injured on special teams. Um, that's why he tore his uh His a cl mcl whatever it was Um, lorenzo telephea. No, lorenzo telephea was decent.  We're not about that man. We're not about that We don't come on here and promote your channel, man. We don't do that, man I appreciate you coming through and I've seen you coming through. Thank you. But we're not about that, man No, dare you store it coverage Coverage he was he was bad, but he could hit and then I I can never and I was just watching it I think I was watching it yesterday or on friday. I can never um, no a knight you don't apologize for that Ain't nothing I can never I couldn't say he was one of the worst in ravens history Because he sealed that stealer's game where we came into pittsburgh and beat up on him and the last playoff Was that the last playoff game we were in? Oh, no, we because we played the patriots after that. So no, um, but yeah Now it's all good here. Yeah, it ain't it ain't nothing. I know he'd be coming through on the videos He'd be coming through but yeah, man, we don't do that But y'all parents or was he just not giving a good shot?  So he missed it second. Yeah, he was doing his thing But then the third year just time opportunities all that stuff dropped and That was it the vaude darling. Wow. Is he was a tight end, right? Wow I hated him and made it. I hated him and made it But this ain't about matter. Yeah, ever done was Elvis. Don't feel was nice man. Elvis. Don't feel was nice again, I was watching the good old days, um We had doom and feel and suck. We got to the playoffs. We beat up on the Steelers We be we should have be done. We should have beat the Patriots, but I mean, it's all good. Oh, Trent Richardson. Yes That was one Trent Richardson His career, I mean with him with the Raiders didn't work out and then he came to Baltimore trying to get another shot and It was just resting peace at that point, man um Yo, they retarded his growth. You talking about pairman leon um Cash money said always see you driving from work. Hey, yeah, that's what most of the videos be at either driving to work or On a break at work or coming home from work. That's where a lot of the videos be it So cash money probably feel like it's kind of weird to see me not in the car right now That's how it be man. That's how it is That was clock I don't that was clock wasn't one of the worst even though he did drop one of lack of easiest touchdowns against the Broncos And then from that point on that's when the Broncos just took off We could have came back the game could have been a lot closer to halftime, but it's all good He wasn't one of the worst players Now he wasn't one of the worst He was just one of the slowest Dallas clock ran in slow motion He ran in slow motion. Whoa clans more shout out to all six for six of them. I wonder what he's doing I wonder what a lot of these guys are doing now clans more could go up there. Um We did talk about ten and all's minus when tory smith got his two touchdowns against the past Hold on what we what we changed this to favorite games Um Okay, oh harry just asked that what's in my favorite regular season game ever um That was one of them when we beat the Patriots, but my favorite regular season game ever was when we were in pittsburgh against the Steelers and um, it was sunday night football when tory smith Toysmith had actually dropped what would have been the game winning touchdown Um two players earlier. So then two players later flakko say, you know what trying to throw the tory smith Was so nice i'ma do it twice and he threw two in the second time and tory smith caught it in the back of the end zone Did the ravens have jim harbaugh? Yeah, they had him as a quarterback Yeah, man, but that was that was my favorite game. He said favorite regular season game flakko santiago favorite regular season game um But yeah favorite regular season game that one would be it. Um, another one would be when we played the jets Um on sunday night football again, uh, that one was in baltimore. That was my other another one of my favorite regular season games um What's another one? The 35 7 Steelers game, um, was that one of my favorites? No, that wasn't one of my favorites.  That is a great one. Actually who said michael hoff michael hoff. Yes michael hoff michael hoff michael hoff. Thank you. That was a great one. That was a great one. Um, what's up? Why? What's going on, man? Mine's 20 point comeback versus. Seattle back. Oh you went through back One of my favorite comebacks from the ravens. It was way more recent though with flakko When they played they played the cardinals in baltimore They played the cardinals in baltimore and we were down like I think maybe going in the halftime maybe like 21 7 maybe 28. So I forgot how much We were down by but they came back. They just kept stomping and crawling back and it was um It's crazy because I had to drive from uh during the game um During the game I started watching the game and then I had to go to my grandmother's house And it was like a 30 35 minute drive from where I stayed at to my grandma's house So I I drove there and I think I was trying to listen to updates on the way there or something Or maybe I was looking at my phone or whatever Um, so when I was on the way there ravens were down big and then while I was driving Then they started coming back coming back coming back and now I got to catch the uh The uh the end of the game and it was just so much fun, man. We came back. I mean one. It was great, man Um, the rookie boy we had last name was cleven clay. You talking about drape? Cable and clay Leon say huff was good and mad. Yeah, he did get some picks man. Was in the 2009 I don't remember the year the cardinals game. I don't remember the year if that's what you're talking about jail Uh, jump off big Sean said my favorite regular game is when the Patriots were going undefeated and oh That game That's the game I got fired from my job for because I took a four hour lunch break. I went to lunch and I didn't not want to miss that game. I went to lunch watch the game And I I said, no, I can't go back to work and miss this. I can't go back to work and miss this I can't I couldn't and I didn't and I don't regret it. But man that game. Yes, that was That was one of the most the games that just Took your heart and just threw it up and Dropped it That game man. Oh That game was pain man because it was um, that game was pain man. That game was painful because um me I was Watching football And live and I was living in Miami at the time and And Oh the shantella thing had happened So that that hit me the shantella thing had happened. So I'm like, man, this dude is from Miami Um, I and I love shantella. I had love watching him. Um, because this dude was just He was just amazing man. This dude was amazing. He was a beast of a player I used to love watching him on the Redskins. I used to love playing with him and madden I used to love shantella man that dude was a monster and then When that thing happened it like it felt like it was a dream when he got shot When he got shot and then because it was all on the news I had because I had worked the overnight shift I worked the overnight shift and um No, this is uh, what's the name? Ronnie Stanley, um, I worked the overnight shift at the time So I worked from seven to seven seven p.m. To seven a.m. And then I used to always go to burger king when I got off work So I went I went to burger king got breakfast and came home and I was getting ready to play madden But then I turned on the tv and the news was on and they were talking about oh, yeah NFL Redskins player shantella has been shouting his home and I'm like man. I'm like wow like wow, that's crazy Like this dude is from here and he got shouting. He's he's an NFL player. So it's like it's like I just felt like I could relate to um Not relate, but I was I felt like uh, like man NFL something I love watching Miami somewhere where I'm living and I'm like man all this stuff is just like it made it feel personal It made it feel personal and I was sad. I was like sad and shocked at the same time and um then that game that game was What was that game? Me like it was like within the the week or two of that uh when shantella got hit but um, I mean when shantella got shot, but um I remember before the game they showed ray louis air read and willis mcgahey and we had on all black that game Was that the debut of all black jerseys? I think it might have been but i'm not a hundred percent sure But we had on all black that game and ray louis and shant I mean ray louis air read and willis mcgahey were all talking to each other and ray louis were praying or whatever and That was it was just sad man. It was sad. I mean all them dudes are from Miami They went to the u and shantella did too. But um Yeah, I just watched black panther like I just saw it for the first time like three and a half weeks ago and it was really good Um, but yeah, it that oh that was sad. It was sad sad sad and um Yeah, that that game that just that alone was already emotional enough, but then The whole shantella thing that was already emotional enough then seeing ray louis and air read and willis mcgahey before the game And then on top of that just how that game went. Oh boy. That was a rough night That was a rough night anybody that remembers that night who Just and you could watch highlights from the game and and you you'll see You if you if you didn't watch it live Then you may not be able to it might not bring up them emotions for you And it may not bring up the memories for you, but if you watch it live man Oh that thing was crazy and then um Then on top of that just the way that the game went and the way that it the last just two minutes of the game Stopping the patriots on fourth down and watching rex ryan call that time out It was just like man Seeing the it was such a bad. It was a passing appearance call that they called um against us I think was it christmas catalyst? I forgot who it was that was trying to cover randy moss and they just could not They just could not they could not they couldn't they couldn't cover moss, but I think it was i'm pretty sure it was a bad call It was a real bad call. Um, oh that game was just oh, it was a lot man It was a lot because it's like man, we got a chance to knock off the patriots and man Oh that game. I'm I think I'm gonna watch I gotta watch highlights of that and then it's like we the patriots They ended up um They ended up getting a touchdown So they took the lead So then it's like a lot of people would have been like oh it's over But then car baller throws his hell mary and mark clayton catches it like at the five yard line Then tries to back in but the patriots pushed him out and it's like man We came that close to still even winning after everything and through everything through all these bad calls through all this Craziness through the rex ryan time out through everything. We still almost won and it was crazy, man Oh, that game was that game was too much So, yeah, anyway, wow, we got to talking about that game for a while um last reluis last home game versus titans Oh, that was your favorite regular season game That's home game versus titans When you play titans in the super bowl year I don't think we did I don't remember though. I don't think we did but I don't remember for sure. Well, what are you talking about though? Bro, that was an amazing game. Did you see willis run that game? Yeah, that game that game was that game was nice, man. That game was great It was great. It just ended the wrong way But it's all good. That's part of football man football is emotional football will drain you Football are you in the school with mark clayton? That's what's up, man When we beat the raiders and tony serguz and knocker again Um, he means coats. Oh, if okay if you talking about coast and I get it Um, okay. He's yeah, he's talking about coats. Okay. Yeah that game whoo Well, I told y'all about this story already I just go back down memory lane again because that was obviously the super bowl year That was a playoffs. That's when ray Lewis had already told us. Oh, yeah, um I'm from Maryland, but I live in Florida Uh, but I ray Lewis had said he was gonna retire and whatnot. So he's like, oh man, that's nice Um, well not nice, but oh, that's crazy. Like we ain't gonna have ray Lewis after this year So they all went all out and whatever and there was his first game back So I had really really really really really wanted to go to that game I had really wanted to go to that game.  We'll be fine. We could just we could do this thing with one car. We'll be all right We obviously ain't have caught at the time. Um, and I was like, yeah, I say, yeah And I took pictures of the car. I put it on craigslist And I left it on there for a little bit not too long, but Then I was just like I say, you know what? I I can't do it. I wanted to I was looking at playing tickets We're looking at tickets to the game I was just willing to I was willing to sell my car Just to go to that game because it was Ray Lewis last game, man It was a playoff game. I knew that atmosphere was going to be crazy, man and just watching it on tv it wasn't And thinking going thinking thinking about it now if I can go back would I have sold my car? No, man. Um, I wouldn't have but If I would have I probably I wouldn't I wouldn't have regretted it because Just watching it if I would have been looking at that footage because I remember we did go to a game earlier that year We went to the Raiders and the Raiders and Ravens game where they beat them like 55 to 20 something Um, and that's on a youtube channel too. Y'all can look at that video if you want to it's in the vlog section So go to the vlogs playlist and you'll see it there. Um But Yeah, that ooh that almost happened just Trying to sell the car just to go to that Ravens game But it just it wasn't just any Ravens game But it was Ray Lewis last home game period and man, that was crazy. They played in Baltimore the last um but For that game against the Colts um Rg3 Andrew But for that game against the Colts Ray Lewis last home game that thing was crazy I remember watching I was crying when he came out the tunnel when they did the entrance um and when uh I remember when Andrew Luck it was a pass. Andrew Luck dropped back and I forgot who hit him But they got pressure on them. They got pressure on them. They hit them. Andrew Luck the pass Flew short and then hit Ray Lewis right in the chest and this dude, man He almost caught a pick and he dropped it. Oh, I I know everybody would have went a while man That's this this all the bleachers in the stadium would have broke The band would have they would have came out on a field playing that that stadium would have went insane, man Insane. Hey, what's up, Koleppy? Oh, man when he dropped that pick and Ray Lewis, he came back looking like a beast, man He had got fat. Uh, he he had the little the the arm thing looking like the shredder from uh Tina from turtles to Uh secrets of the ooze. He came back looking like a beast, man beast And man that was crazy And then I remember too when he um And after we after the game was over and we were taking the knee and then he came out and did the dance Or the oh man.  But yeah, now you're right. You're right, Michael. Now can't stand Ray Lewis While he was playing Oh, love you after he stopped playing Can't stand him man.   Do you think uh Jalil Scott can start? No, he won't. Um, it'll be crab tree It'll be crab tree. Maybe brown and sneak um You was tearing up on Steve Smith's last game.  That's the perfect way to describe it Michael. He feels entitled. That's perfect We almost lost half our team after we won the Super Bowl. Yeah I mean, that's the price of being successful, man Ravens have always I mean, well usually uh More so around that time frame by 2012 and before even a little bit after but more so before we We had been so successful Over and over and over and over again that Our free agents they and they always say, you know, they price themselves out of Baltimore. It always happens. Oh, man Nitro, man, you got to stop with all this, man I try to say every time you put a comment, man, just they'll be getting too deep for me sometimes, man, but that's That's true. He say Ray fell in love with Ray and the statue didn't help Whoo, he did it again, but yeah, man That's that's true. I can't say nothing. That's true. It's true. It's true um I'm I would be against a statue for anybody because I don't think anybody is worth a statue because that's But that's a whole another subject, but um, yeah Ray little them doing that for him is Anyway, anyway, um I looked up our schedule Do you actually have five preseason games and who'll be our quarterback for them? Yes, we do have five preseason games polo because one of them is a Hall of Fame game Okay, jump man already answered. I need to see the comment yet. But yeah, one one is the Hall of Fame game and um The other four regular preseason games Flacco is probably gonna play He's not gonna play in a Hall of Fame game. He'll probably Maybe week one, but I think definitely week two definitely week three Um, and I am actually in the process of looking up tickets for that week three game for the Dolphins So the post game stream, I don't know how that's gonna work out. Uh, well, that's if we even end up going We'll see how stuff works out, but um All the fame game. I think it'll be rg3 and Lamar Jackson or rg3 and Woodrum Um, I think it will be rg3 Lamar Jackson and Josh Woodrum. Um, I think all three of them are playing that game um and For the week one, we might get a little dose of flacco, but definitely the backups too Um air read plays praise Lamar Jackson saying here. Oh, he did. Okay. That's what's up, man See, I take that from air read if it was Ray Lewis, I'd be like, uh, you're just talking You're just trying to get some attention but air read air read. I love air read before He's retired and after a time because air read just stays low key man. He stays to himself He don't say much. He don't come around much. He's not in the spotlight much Air read just stays to itself doesn't sting doesn't say nothing And but when he speaks he don't say crazy stuff. He just chills, man Where the day's confirmed for the Miami Baltimore preseason game this year. I'm pretty sure they are already Yeah, I'm pretty sure they are already Oh, you see, I love to see Lamar start week one and play Josh Allen Hey I doubt it's gonna happen, but you never know you never know until it's all said and done. You never know Um, so we'll see what happens. Yeah, air read is awesome, man But yeah, I'm pretty sure the dates um The date the dates for the games are already confirmed. I believe let me see if I can Oh We missed it went in and out. It looked like one of those carnival games Okay, I just got cheated by my son basketball, man. It is what it is Um, ace of jackson. Yes, that's definitely one the Raven play the Chargers here in LA this season Oh, yeah, go man.  Yeah, man. Chris redmond. Oh the quarterback. That could be one I could definitely be one. That's my favorite rate of Michael Craitree. Get him. Hey, we trying Rob Trying that look like oh kwami brown. Wow. Shout out to kwami brown Shout out to the washington wizards, man kwami brown kwami brown Hmm Yeah, sherry's right. Definitely. Yeah lorenzo telefield.  I don't think lorenzo though But I give I mean, it was right. We talked about that man. Ray Lewis Hall of Fame speech It's gonna it's gonna be What's the record like an hour and change Ray Lewis is gonna double that he's gonna double that Hey, appreciate you young savage. Thank you Ray Lewis is gonna double that he is going to double that he's going to it's Man, I think what who broke who set the record was it Brett fall for whether somebody I forgot I don't even care who Ray Lewis is going to break that record and it's not even going to be close. So anybody who Yes, it's going to be more than a sermon. It's going to be Ray Lewis is going to talk an entire bible Um, it's uh, man, I'ma watch it now. I'ma watch it, but you know what? I don't know When when will that be because the game is on a thursday night, I believe Um, so the speech will the speech be on a wednesday The game is on a thursday, so I gotta see the schedule Oh, it's on tuesday the speech is on tuesday or the induction ceremony or whatever. It's on tuesday Wow You say as long as As long as the national anthem by Rita Franklin I was out of town for a game So I watched the live stream on youtube they kept getting cut off because of copyright You can't watch games on youtube. They will get cut off. Um I mean because and the worst is when you're watching I try to I try to do it last year I didn't I didn't do it successfully every game last year, but no, you know what? We did do it for the most part though But for the games last year I try to put out a link to the stream that I'm using because they work They usually work through the whole game But You you can't watch them on youtube because this happened to me before and it's going to happen to youtube You'll be watching the game and youtube Excuse me, whenever people stream the games on youtube Um They the quality of it is great. It moves smoothly. It's running smoothly. It's like oh, this is great, man You'll be so into the game. Then all of a sudden boom copyright stream shut down. So Don't I don't even get start watching on youtube because you're gonna be heartbroken because you'll be so into the game It'll be in the middle of a play. It'll be in the middle of a play So youtube ain't got no mercy. They don't care. They don't care. Well, I appreciate that polo. Thank you, man Uh, do you think reloose is the best linebacker ever? I don't I mean numbers kind of back it up. So yeah, yeah Um, no middle linebacker know what? Yeah, that guy lay loose, man. Is ray gonna do his dance?  Of course he's gonna do it for hall of fame, but What what I said before on other streams or other videos or whatever. It's like It sucks because it's it's like a lose lose situation for all of us Um, or anybody that doesn't like him him talk over no, but It's it's like a lose lose situation for us because one this is gonna be ray lewis is going to be the last one to go up um This is Yes Okay, I gotta keep the camera on me. Yep, of course. Yeah, that's carter this Your team keep it all the way clean, huh son Hmm Anyway, um, he He's gonna be given a platform to talk about himself And that platform is it's gonna be uh, it's gonna be a long it's gonna be a long night But here's what it is, man Appreciate that radar matt. Oh, it's only one of them though. It's only caught up by himself Airy next year. Yeah. Yeah, he caught a troll in me now Because he came in here now. He's playing his piano. He knows I'm doing the video. He knows that Carter Carter Carter What are you doing? What are you doing? Dude always messing with me, man um So, yeah, anyway, appreciate y'all coming through. Thank you again If y'all want to be a part of nfl question from subscribers Just know that Well, stay down son. That's that's as bad as far as you can go up. You got to stay down Um, but if y'all want to be a part of nfl question from subscribers Uh, just send me a dm on instagram twitter snapchat. Nice your question in the video Um, so yeah, man Appreciate y'all matter stream tonight most likely not I'm about 9.9 times out of 10 Sure that it probably won't happen. Um, but yeah, I don't know You know what happened yesterday So we had went to a graduation party For one of my guys that just graduated from college.  We're all gonna go chill at the house. Um So we went we went we were getting ready to go there, but at the party this one dude was like, um He was like, oh man I'm good at matter man. I don't see nobody in matter I'm I'm serious in it and I and I was looking I wasn't in the conversation, but I heard it I said, oh, I said, whoa, whoa, whoa, whoa, whoa slow down there slow down there and I was talking. I said slow down hold up And I told him I said wait now I wouldn't say that but He said no, no, no I do this for a liver Okay I said we got to play them So we played And he had went up He got the ball first He got the ball first. He picked the stealers. I picked the Ravens. He got the ball first. He scored a touchdown nice drive um, then I got the ball and then Alex Collins fumbled the ball I think it was his first carry if not his first carry didn't his second carry. He fumbled early. So the guy Back to back, then he got another touchdown. So I'm like, okay Cool, and that and all everybody in everybody in the room was all cheering jumping up and down. Oh, yeah, man Yeah, yeah, yeah, I say I say y'all gotta chill man. Just calm down. Just vibe man. Just chill so um Then I got the ball Then I scored a touchdown. So it was 14 seven I was down then he got the ball and he scored a touchdown.  I felt bad for him because he got quiet But anyway, what's my favorite matter never I don't really have one but um, I mean, I like all of them I like all of them Uh Hey Khalil you just might I'm on xbox one though. It's uh, it's engraving. It's engraving ing rv and Uh, somebody asked something. Will you allow car to play football? Nope No Not at all, man I love football Love watching it And I would I would love to see him in it, but no No I just Because if if he took the wrong shot That's it man And them dudes they know what they signed up for and they got all these new rules to be safe or whatever But football is not a safe sport. It's not it's not a safe sport No matter how many rules you try to put in the football to try to make it safe It's not a safe sport. It's a physical sport. It's a contact sport. It's a violent sport So no I wouldn't I wouldn't Um soccer is growing soccer is big man. They make money in soccer. They make money soccer baseball basketball All that stuff, but He said really wow dude qb. I played for 15 years. I'm good. That's fine. That's fine.  That's fine. This is my son. No, I wouldn't so that's fine So he said even if you became a raven See yeah, and you saying you played quarterback for 15 years You just never took the wrong shot. That's it. That's it That's fine I know I my boy smooth. He played football. I'm sure a lot of people in here play football too. That's fine But yeah, I I wouldn't I wouldn't Lamar will be on a madden cover someday as a raven. No, we don't want that We don't want that.  We don't want that Uh gavin say all it takes is one wrong hit and you're in the wheelchair. Are you ready for another song? Yeah, he said you get Carter Jersey. Appreciate that. That's your hammer But yeah, I let him play madden. He can play madden all day, man He can play madden. Oh, Michael said I took several shots and nothing is good about it Yeah, man, and it's the game is different now too, man, because these guys We banging on the floor these guys are bigger faster stronger So and that's why people are getting injured at these alarming rates because people They their bodies are just different. I feel like people bodies on as as developed as they were before man Because people just it's crazy, man But it's all good, man He gonna oh, he's gonna be a man when he get he probably beat me a matter now if he lined up, man I love love to if you didn't oh if you didn't have scoliosis or you love to play football there We winding up, man Football is a battle every damn man. Oh man. No mercy dangerous game. Yeah, it is man.  Some of y'all go went in and made it out just fine That's fine. But no, I wouldn't even take the risk for for Carter I hope taevon young does good man. I really hope he does. I really hope he does Oh, okay. You had the scoliosis early then. Well, that's a good thing, man I'm glad they didn't let you play because that could have made it worse So good thing, man. Do I see flacco getting benched? Only if he just is just absolutely terrible and it's and it's his fault that he's terrible. What's up, Francisco? That's the only way I see flacco getting benched. See what happens when I try to end these streams I try to end the streams in we never end them when we say we're gonna end them, man Only one percent make it to the league but I I Oh, you got a coach after okay. You could do that, man I hate to stay loose, but pray for chaisea I mean, yeah, I just hope I hope he gets his health All the way because I see he's he's walking now. Well slowly, but he made a lot of progress, man He made a lot farther than a lot of people thought he did including myself Then a lot he made a lot farther than a lot of people thought he would excuse me The guy from Rutgers took the wrong hit and will never walk again Is that the black the black guy with the dreads in the wheelchair? Is that him? So what is it then if it's not a t-rex? You said this is a velociraptor Yeah, you're right. This is not a t-rex though. So I agree Carter Um It's like all sunday barbecues always get better at the end I like that man. Appreciate that one Do you think we have a chance of making it to the super bowl this year since we have better wire receivers? What'd you find? I think we do It's just a matter of just closing out games This is a matter of being balanced on offense and defense The offense actually helping out the defense and the defense continuing to do what they've done for the most part over the past couple years, man so Here's what it is No, it's that guy they got hit by a kicker No, I don't even know the silver game with macklin dropped the pass and laid laid on the ground like he Oh, that wasn't the last stealers game What is it? Oh, it's a controller. That's what it is. Whoa. Whoa. Don't fall. So Very right to alice collins. Very right um I'm still a fan since the 17 since the 70s lamar jackson will be playing early the season joe flacco gets hurt every year Just like but no Flacco never get hurt Flacco never gets hurt man Flacco's all he's always healthy the only time he missed games is when he toys acl flacco's always healthy He's always healthy. Um Yeah, the only time he got hurt was yeah when he toys acl and then after after he tore his acl. He still played three plays so, yeah now For injuries and then last year his back he had little back spasms or back pains or something like that, but That he just missed a preseason for that. He ain't even missed no regular season for that But yeah, and macklin used how he used catching with xbox control. I don't know Man macklin was just he was just bad for us man. You think crack tree will be a thousand y'all receiver You know, I think you get about like eight or nine hundred. I don't think you'll get a thousand if he does I'll be happy. I don't think he will though. Hey, no problem.  You know, yeah macklin, uh Yeah, that costs us a time out too. That costs us a time out man Cost us a time out things you can't grip and we'll have one hand on matter. It will look like a Wow, that's a good question That's a good question Really quick. Oh god, what are we doing? You know what? Let me look at my dm on twitter real quick because somebody wanted wanted us to talk about shakim griffin one second Okay, there it goes. So it was my guy king swaggy p. He said can y'all talk about shakim shakim griffin In a live stream. So yes, we're doing it right here at the 51 minute mark. That's what I'm gonna tell him when I send him this video so he Will he have one hand in matter? That's a good question I think his speed is gonna be like an 88 though. He's gonna be a fast line But you know people gonna be putting them in too people gonna be putting them at a metal line back on username with them I know I will be if I play with the seahawks. Um, but yeah shakim griffin Uh, get to play with his brother. That's that's fire man. That's the best. He get to play with his fire. What's your idea? What's your idea son? What's up, qc? So yeah, shakim griffin, um, I hope he does good man.  Orlando brown. Are you talking about? What Orlando you talking about? um Terrell you said exactly what you're talking about. Terrell grab tree will do better because uh to leave isn't Ah Yeah, man, we got we got we got the guy that's been getting his chain snatched man So it's all good, man. If you got 10 000 to take the hit from Ray Lewis in this prime, would you? Uh, yeah, I would I would I'd be I'd definitely be Have a bunch of pads on me. I would uh have extra pads on me that the NFL didn't even know about um, I would Yeah, I put extra cushion in my helmet. Um, what's up savage?  Yeah, man Hey, ready to man. Are you excited? Oh excited for Martavius Bryant. Um Martavius Bryant man. He oh I like him. He's nice. He can make all the catches. He can run. He got speed. He got size.  Carter. That's not a raven. That's an owl man Uh, go ahead.  Don't try to scare me. Do your thing Come on. What's the owl saying? Why are you just why are you trying to scare daddy? He wants to tell him. Tell him what What is he want to go? You see you later everybody See you later everybody To buy ravens fans Oh, you ain't had to give everybody a kiss Okay, that was nice Okay, see you later guys So team keep it clean Okay, thank you. I love you All right, but um Appreciate y'all Which corner do you think the ravens are part with before the season starts? Um, maybe canady Maybe canady um, but anyway Team keep it clean. Appreciate y'all. Thank you all for coming through. Thank you for watching. Wow. It's already been an hour. That's crazy. Wow That is insane. Um, I didn't even realize it had been that that long Um, but appreciate y'all man. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you Um, again, make sure you subscribe if you haven't already turn your notifications on if you haven't already Carter, you want to come say bye one last time? Come here. Okay, whatever All right, appreciate y'all man Why do you keep doing it? He keeps pushing the door open and then closing it Come here. All right. He's gone. All right. Appreciate y'all man Make sure you subscribe turn notifications on and follow on to it just in case youtube unsubscribes you or if you unsubscribed already Hmm. I wonder if some of y'all are doing that But anyway, appreciate y'all. Thank you. We're going man. I'm by


I hope everybody had a nice holiday weekend and got rested up for the spring finish. We have two more weeks for the first time in, I guess, three weeks. We're going to have a full schedule this week and then also next. And as you may recall, last week before we left for the break, we're talking about various kinds of matrix manipulations and some matrix mathematics. And so what we're going to do today at the start is we'll finish up with the background on matrix manipulations. And in particular, we're going to talk about a very important class of matrix equations which are called eigenvalue equations. So I'm going to start by sketching what the problem is on the board. And then we'll explore what I explained to you now using Mathematica. OK, so eigenvalue equations are ones for which we have a matrix, which I'll call capital A, and denote with double squiggles. And I'm going to assume that this is a square matrix with n rows, little n rows and little n columns. And now if we multiply that by a vector, n-dimensional vector, so this is going to be a vector that has n rows and one column, then if that can be written as a constant, which I'll call lambda, times the vector itself, this is what's called an eigenvalue equation. OK, and lambda is what's called the eigenvalue. All right, now these types of equations arise in many, many places in physics and chemistry. And those of you who are in Chem 131 right now, you know about eigenvalue problems in the context of the Schrodinger equation, which you're going to learn about in Chem 131B is a matrix formulation of quantum mechanics in which the problem can be expressed in this form. The problem of determining, say, the electronic structure of a molecule and the energies of the orbitals. OK, in fact we're going to do an example shortly, probably tomorrow, from orbital theory of aromatic molecules, and that type of problem is one that you will cover in some detail in physical chemistry. But the bottom line is there's many, many problems that can be expressed in this form, and so it's useful to understand how it is that you can determine these values, lambda, because that's one of the quantities that you're typically interested in determining in eigenvalue problems. And then as well, the values of these vectors, which are called eigenvectors, is also part of the problem. OK, now, just a quick crash course on what one actually does if you want to try to solve this problem. So first of all, we can write this equation as A minus lambda times the identity matrix times the vector eigenvector is equal to zero. So all I did was move the lambda x over to the left side, and this just turns lambda times the identity matrix is just a matrix whose diagonal elements are lambda. So this is a n by n identity. All right, so now what we want to do is solve such an equation to determine the lambda, that the lambda will solve that equation. Now, one possible solution is that x is a vector with all zeros and zeros, and that's what we call the trivial solution because it's not interesting. OK, so for non-trivial solution, the way we can get the lambdas that satisfy this equation is that it amounts to saying that the determinant of A minus lambda times the identity matrix is equal to zero. OK, now, it may not be obvious, but when you actually form the determinant and solve this equation, what this is going to give you is n roots, which we can label lambda i, i equals 1 to n. OK, because this determinant equation here will give you an nth order polynomial in lambda. So that's essentially how you determine the lambdas. Now, to determine the eigenvectors, the various x's, so now there's going to be, as well, n vectors x that satisfy the equation, one for each lambda. We need to do a little bit more work. So recalling that there's one of these equations for each i, we can actually collect all of them together by saying that A times now a matrix, capital X, is equal to a matrix lambda times capital X. And what this x is here, this is a matrix formed by taking each of the x's here. So there's x1, x2, x3, dot, dot, dot, xn. And I'm going to put them as columns into this x matrix. So we'll have x1 vector x2 vector dot, dot, dot to xn. Okay? So these are each n long. So we've formed a square matrix that contains all of the x's that satisfy this equation, well, this equation. All right? And then this is a diagonal n by n diagonal matrix with elements lambda i. All right? So we'll see this explicitly in a couple of minutes. All right? So this now provides the basis for determining the x's. And here's how we do it. Okay? So first thing we do is we're going to multiply through both the left and the right hand side by the inverse of x. All right? So if we do that, then we get x minus 1 a x is equal to, since this is a diagonal, it can be moved out here if we want. So that would be x to the minus 1 x lambda. And x to the minus 1 times x is just the identity matrix. So then this gives us lambda. Okay? So here's the punch line then, right here, for how you determine the x's. Okay? What you want to do is find a matrix x that by the process of sandwiching a in between its inverse and x, you create a diagonal matrix. Okay? So in the language of eigenvalue problems, the matrix of eigenvectors x is the one who diagonalizes the matrix a. That's the language that we use. All right? And this particular process of diagonalizing a, see, by sandwiching a between x to minus 1 and x, we get a diagonal matrix. This has a name that's called a similarity transform. Okay? So just to recapitulate how it is that we solve eigenvalue problems, and you'll see we don't actually have to solve them because Mathematica will do it for us easily. But just to give you the background, we have a general problem like this. Appears many places you'll see in physical chemistry. All right? You solve this polynomial equation and you get the lambdas. And then you find the matrix x that diagonalizes a. And then this gives you the columns corresponding to the vectors x1 through xn. All right? So let me just give you one quick preview of what we're going to do probably tomorrow. So the problem tomorrow is going to be, this is going to be Hamiltonian. This is going to be wave function or orbital coefficients specifically. This is going to be an energy of the orbital. And then this is going to be the orbital coefficients. All right? So this, you can write quantum mechanical equations for the energies and orbitals of a molecule in matrix form. In fact, when you use Spartan, all of you have used Spartan I presume, you're essentially solving such an equation on the computer. Okay? So we're actually going to do that tomorrow. But for now, I just want to explore some aspects of the eigenvalue problem and show you how to use Mathematica to solve it with some simple examples. So let's go ahead and do that. Turn on the screen here. All right. So we're going to start really simple. We'll just do a little 2 by 2 matrix. And so I'm going to define the matrix A equals, curly, curly, it's going to be, the first row will be 1, 2 and then the second one will be 3, 4. All right? And now we can look at A in matrix form. And so there it is. All right? Now, we don't actually have to do this to solve problems, but I just want to show you some detail of how it works. That equation over there that says debt of A minus lambda times the identity matrix equals 0, that's what's called a secular equation. All right? So let's go ahead and see what that looks like for our matrix here. All right? So I'm going to define secular equals determinant A minus, and then we can put a lambda in there if we want, lambda times, and to get an identity matrix with n equal 2, we can say identity matrix bracket 2. All right? So that just gives us a 2 by 2 matrix with 1s along the diagonal. All right? So if I enter that, notice I get a quadratic second-order polynomial equation for lambda. All right? So these secular equations for an n by n matrix end up being nth order polynomials, which we could solve if we want. We'll see in a minute that there's a quicker way to get to the answer. But just to show you how it works, we could say solve secular equals equals 0, and then we're solving for lambda. So how many roots should we get? Should get 2, and those are the two eigenvalues that satisfy the equation that matrix times an eigenvector is equal to eigenvalue times that eigenvector. Okay? And just for completeness, I'll show you another way that you could generate the solution or the secular equation in Mathematica. You could also say secular equals, and there's a command called characteristic polynomial. It's a lot of typing. And then you say what the matrix is and then what the variable is. Okay? So this gives exactly the same thing as here we formed it by hand. We said give me the determinant of a minus the eigenvalue times the identity matrix. This command here basically just does that. Okay? All right. So the point of this is to show you that in fact the solution of the eigenvalue problem for the eigenvalues consists of finding the roots to this secular equation. Okay? Now, there's an even easier way to do it, so in general you're not going to do this, all right? This is just for illustrative purposes. If you have a matrix, a square matrix, and you want the eigenvalues, you don't need to go through this business of setting up the secular equation and solving it. Mathematica has a nice little command that allows you to cut to the chase and so you could say directly, for example, lambda equals eigenvalues of A. All right? And when you do that, you see that you go directly to the solutions of the secular equation, all right? So when you want to calculate eigenvalues with Mathematica, just use the eigenvalues command. Also, you may want the eigenvectors and the way you get those is you just ask for them eigenvectors of A. Now, what should we get here? Let's think about what it is that we should get. Anybody want to venture a guess? All right? We have a 2 by 2 matrix. So how many eigenvectors are there? Well, we've seen that there's two eigenvalues and for each eigenvalue there should be an eigenvector. So we should get two eigenvectors and each of them should have length 2. Correct? All right? So let's see then what we get. And what we get is, in fact, a list of two eigenvectors. The first one is here. It has first element here, the second one, and then the second eigenvector is here. Okay? Now, I personally like to get the eigenvalues and eigenvectors separately because they tend to be useful when they're separated. But if you wanted them all in one shot, there's a command called eigensystem. All right? So if you say eigensystem of A, what you get is the whole collection, first a list of the two eigenvalues and then the two corresponding eigenvectors. So this eigenvector corresponds to that eigenvalue and this one to that one. Okay? All right. Now, the next thing I want to do is I want to show you, we're going to verify this similarity transform. All right? So what I want to do is I want to show that if I form a matrix X whose columns are going to be first this one and then this one. So what I'm going to do is I'm actually going to transpose these. This is a row vector now. I'm going to transpose it into a column and I'm going to pack those two into a matrix I'm going to call X. Then, we're going to calculate the inverse of X and we'll multiply the inverse of X times our original matrix A and then times the matrix X and we should get a diagonal matrix whose elements are these guys. All right? Just to show you that it works. Okay? So here's how I'm going to form the matrix X. So, X equals transpose and then the eigenvectors of A. All right? Put a semicolon and then we'll look at it in matrix form just to make sure it looks right. Okay? So now notice this eigenvector has been put like that and it now shows up here. That's X1. Okay? And then this one has been transposed and put in here. X2. All right? So X1, X2. So that's our matrix of eigenvectors. All right? Now let's go ahead and get the inverse. I'm going to say XINV equals inverse of X. Okay? And then what we'll do is we'll say XINV dot A dot X. And I'm going to put that in matrix form. Okay? And the similarity transform tells us then what I should get out is a diagonal matrix whose 1, 1 element is here and 2, 2 element is here. And maybe we need to simplify. Oops. Okay. So there you have it. We force, by putting this in here, we force Mathematica to do some algebra to clean things up. All right? So as advertised, 1, 1 element is the first eigenvalue and the 2, 2 element is the second eigenvalue. So you see that it works. And what I hope you see even more than it works is how easy it is when you have a tool like Mathematica. Has anyone in here ever solved eigenvalue problem by hand? I know a couple of you have had linear algebra, right? And it tends to be, well, for 2 by 2 it's not so bad, right? But it quickly becomes very unpleasant as you get bigger and bigger matrices. So this is kind of nice, huh? Yeah. All right. So that's a simple illustrative example using a 2 by 2. So the next thing I want to do is we'll just make a slightly more complicated example of a 3 by 3 just to walk through and do it one more time so you see another example. And then we'll have covered all the material that you need to know to do your homework. So I'll go over the homework assignment with you. All right. So now I'm going to define a 3 by 3 matrix. I'll call it A again. A equals, curly, curly. And this one's going to be, first row is 1, 2, 3. Second row is 2, 2, 2. And the third row is 4, 3, 3. All right. So let's just have a quick look here. By the way, let me, I want to preview a very common error that can be made that can be a little bit difficult to track down when you're working with matrices, all right? So I don't know if you've noticed, but when I enter matrices I enter the matrix and then I look at it in matrix form. So let's do that here. Okay? All right. So there it is. So this defines the matrix properly and this lets me see it in matrix form. And once I've got the matrix in there I can do stuff with it. So for example I can say, give me the determinant of A. All right? And I get a number as I should. Now what you should not do is you should not do something like this, define a matrix in matrix form, all right? See the difference here? Here I'm actually setting A equal to the matrix form of this matrix. This is a graphical object. It's not a mathematical object in Mathematica. So watch what happens if we do that. It looks fine, but now if I try to get the determinant, I get the determinant of a graphical object which doesn't make any sense. Okay? So this is just a warning to be careful. I think it's always nice to look and make sure you entered your matrix properly by looking at it in this format, but always do it after you define it. Don't set anything equal to a matrix form. Otherwise it's unusable for further calculations. And it's something that's done commonly and when I was working on the solutions to the homework I did it myself and just be aware that that's a common slip up. Okay. So let's go back and clean this up. Put it back in matrix form. Okay. All right. Now I'm going to just go ahead and directly get the eigenvalues. We'll set them equal to lambda. That's a common notation. All right. Did I make sure I enter this? Okay. And notice that I get something interesting. All right. Now it kind of looks weird. And it looks weird because there was no sort of exact form of the roots for this. It's going to be a cubic equation. Or at least it's not able to spit that out. Okay? That's not a problem if you don't mind working with numbers. Okay? So what I could do is say, instead of saying lambda is equal to the eigenvalues of A, I'll just go ahead and put the N command out in front and I'll get some numbers. All right? So I should get three numbers, three eigenvalues because I have a 3 by 3 matrix. All right? So now I get the three numbers. Okay? Now let's have a look at the eigenvectors. All right? And you see that also looks like garbage.  And we get as expected three vectors, so a list of three vectors, each of which has three elements. All right? Because we're working with a 3 by 3 matrix. Okay? So if we were interested in solving the eigenvalue problem for the eigenvalues and eigenvectors of this matrix, then we're done. See how easy it is. But again, just for fun and for practice, let's go ahead and use these results, manipulate them to see that in fact the similarity transform as written over there works. So once again, I'll say x equals transpose I'll leave the N in there, so I get nice numbers. And I'll put a semicolon. And then I'll look at x in matrix form. Okay? So there we have our matrix of eigenvectors. This is x1 corresponding to the first eigenvalue, x2 to the second, and x3 to the third. Okay? We can say xinv equals inverse of x, semicolon. And then finally, let's check the similarity transform, which is xinv.a.x equals, or no, not equals, let's just leave it like that. And put it in matrix form. Well, we'll get to that in a second. All right? And what we see is that we don't get a diagonal matrix of eigenvalues, all right? You can see that the eigenvalues are in fact along the diagonal, but then there's these other numbers in here kind of polluting our beautiful diagonal matrix. Now these are likely just due to numerical imprecisions. Okay? So we can get rid of that. By putting in something we've seen before, which is called the chop wrapper, which will remove, eliminate numbers that Mathematica thinks are imprecise. All right? So we can just say give me chop of that. And now you see that in fact we've got a nice clean diagonal matrix whose diagonal elements are the eigenvalues. So once again proving that the matrix X is the matrix of eigenvectors and the similarity transform is correct. All right? So there's your introduction to solving eigenvalue problems using Mathematica. Okay? And those of you who haven't had a course in matrix, mathematics, linear algebra can't appreciate what a wonderful simplification, what a nice tool this is, but I assure you that in fact it is. Now let's go ahead and have a quick look at the homework assignment since we know everything we need to know to do it now. Okay? So the first problem is a problem that is going to involve doing calculations with vectors. All right? So what I've given you in this table are Cartesian coordinates for the three atoms in the molecule NOCl. Okay? So this is X, Y, and Z coordinate of nitrogen, oxygen, and chlorine. Okay? Now each of these sets of three coordinates defines a position vector. So for example I could say Rn equals 0, 0, 0. And R0 equals that, and Rcl equals that. Okay? So R0, Rn, Rcl. Okay? So what I want you to do here is based on these coordinates calculate the bond length of the NO bond. And that amounts to, this is just the distance which is the magnitude of the vector pointing from end to O, which is the magnitude of the difference between R0 and Rn. Okay? So you're going to enter Rn, R0, Rcl. You're going to calculate the difference between R0 and Rn and get its magnitude, and that's the bond length of the NO bond, and then you're going to do the same thing for the CLO bond. Okay? And then finally you're going to calculate the bond angle, which in terms of these vectors is given here, which is just a rearrangement of the relationship between the dot product and the cosine of the angle between two vectors. Okay? Everybody understand what I'm asking for there? All right. Okay, so the next problem, this is just a very simple one but just to get a little practice. So in physics as you probably know, the angular momentum, which is indicated as the vector L here, is the cross product between the position and the momentum. All right? And so if you define R is equal to XYZ and momentum is equal to momentum in X, momentum in Y, momentum in Z, then L will have components that I want you to evaluate. So basically I just want you to enter these two guys using some reasonable notation and get the cross product to see what the components look like. Okay? So that's a very straightforward problem there. Okay. Next thing is I just want you to explore some relationships from linear algebra concerning matrices. All right? So we have two matrices here. I want you to enter those in and then verify so you can calculate AB and then BA and look at them. You'll see that they're not the same. These are not symmetric matrices. They don't commute. So that's just a reminder to you that in general matrix multiplication is not commutative. It's a useful thing to know. Okay? Here's an interesting one. If you take the product of A times B and take its determinant, that is actually equal to the determinant of A times the determinant of B. Is that ringing a bell from people who took linear algebra? Okay. And then you're going to calculate the inverse and show that inverse of A times A is equal to the identity matrix and A times the inverse of A is equal to the identity matrix. Here's another interesting one. If you take the determinant of the inverse, that happens to be 1 over the determinant of the matrix. So I want you to show that also. And then that's it for that problem. Okay. The next thing I want you to do is put in this matrix which has some variable X in it and then just use the solve command to solve the equation determinant of A equals 0. Solve for X. Okay? And you'll get, this is a 4 by 4 matrix so there should be 4 roots and you'll get them. And once you enter the matrix, it should be one line. All right? And then finally, I want you to enter this matrix and then just do what we've done already twice here today. All right? So find the eigenvalues, the eigenvectors and then verify the similarity transform. All right? And this will get you nice and warmed up for doing what I hope will be a fun and interesting problem in next week's assignment where we're actually going to use what we've learned here to solve for the orbitals of a conjugated organic molecule. Okay? All right. So let's see. We've got a few more minutes. So I'm going to go ahead and start with a few miscellaneous examples where we can use some of the things we've learned from the vectors and vector analysis and matrices that are relevant to things that you will see in physical chemistry. Okay? So the first thing is this one's sort of more for your entertainment only. The second example will actually be relevant to a homework problem. I want to revisit the vector analysis package and show you how you can have access to alternate coordinate systems and in particular the spherical coordinate system which shows up a lot in your physical chemistry course. All right? So let's go ahead and load the vector analysis package. So that's less than, less than vector analysis, backward single quote, enter. Okay? And now I'm going to change my coordinate system which by default is Cartesian. So I'm going to say set, oops, capital set, coordinates. And the system we're going to use now is called spherical. That's the spherical polar coordinates that Mathematica knows about. And now I'm going to define the symbols I'm going to use for the three coordinates. Actually, let me go here first to show you what we're doing. Okay? So this is actually what we're talking about here. It's a coordinate system where we go from the Cartesian x, y, z to one distance and two angles. Okay? So r here is now the length of a vector pointing from the origin to the point of interest. Okay? And then we can define two angles. One is called the azimuthal angle theta which tells us how far this vector is, well, what's the orientation of this vector with respect to the z-axis? And then we have this other vector which is called the polar angle which tells us how far or what's the angle between the x-axis and the projection of r onto the x-y plane. Okay? So those of you who are in Chem 131 are familiar with this coordinate system because this is a convenient coordinate system for solving the quantum mechanical problem of an electron orbiting a nucleus, right? Okay. And these are standard notation, r, theta and phi. All right? So that's what we're actually going to use here. We're going to define our spherical coordinates to be r, theta and phi. Okay? All right. So if I enter that, it just says verified r, theta and phi. And if I ever want to know what coordinate system I've set, I can just say coordinate system and it tells me I'm in spherical coordinates. If I want to know the ranges over which those coordinates are defined, I can ask for it, coordinate ranges and if I leave a blank bracket, it will give me all three. And so it tells me that r ranges from 0 to infinity, theta from 0 to pi and phi from minus pi to pi. So phi is the whole circle and theta is the semicircle. All right? Now, other useful things that you can do is you can ask what are r, theta and phi in terms of the Cartesian coordinates? So I can say give me the coordinates from Cartesian bracket and then I list what I'm calling Cartesian. So I'll say x, y and z and I can see here that I'm going to have to clear x. So let's go ahead and do that. Okay? So let's see what this gives us. All right? Now, those of you who've studied the spherical coordinate system before probably recognize these formulas. So this is the definition of r in terms of the Cartesian coordinates, right? It's just the square root of x squared plus y squared plus z squared. This tells you how to calculate theta from the Cartesian coordinates of a point and then this is phi. Does that look familiar to anybody? It should look familiar to those of you who are in Chem 131 at least. Okay? Now, what if you wanted to know how the Cartesian coordinates are defined in terms of the spherical coordinates? All right? The way you could do that is you could say coordinates to Cartesian. And this should also give some familiar. So now we put in our spherical coordinates r, theta and phi and now it's going to tell us how x, y and z in the Cartesian coordinates are defined in terms of r, theta and phi in the spherical coordinates, all right? And again, that's a formula that should look familiar to some of you, all right? So x is actually defined in terms of r, theta and phi as so and then y and z. Okay? All right. Now, just to finish up today, we talked last week about vector derivatives and I'm not going to go through every possible one of them but I'll show you a couple of the ones that are somewhat interesting, especially if you've studied the hydrogen atom in your Chem 131 class. So the first is I can ask for the formula of the gradient of a function, a scalar function of r, theta and phi. Okay? All right and if you enter that, then you get the following. Okay? So just to remind you what this notation looks like. So this now is, remember the gradient takes a scalar function and gives us a vector whose components are the derivatives of the scalar function with respect to the three coordinates. All right? So in the case of Cartesian coordinates, it was simple. This, the first component was just the derivative of the function with respect to x. The second, the first derivative with respect to y and the third, z. Notice when you go to alternate coordinate systems such as the spherical coordinates, the formulas are a bit more complicated. Okay? So this is the component of the gradient in the r direction, which is simple. It's just the first derivative of f with respect to r okay? But then when you go to theta, it's the first derivative of f with respect to theta divided by r. And then when you go to phi, it's the first derivative of f with respect to phi divided by r times the cosecant of theta. All right? And then those of you who are in Chem 131a probably saw or should have seen the formula for the Laplacian in spherical coordinates. All right? So that's del dot del. All right? So we can say give me the Laplacian of r theta and phi. Now this is going to give us a scalar result. And as some of you have already seen, that looks fairly complicated. In fact, let's simplify a bit here. All right. So in any case, notice it's just a single element. So it's a scalar function and here's the part that has the second derivative with respect to phi in it. Here's the part that has second derivative with respect to theta. And here's the part that has the second derivative with respect to r. And then here's another part that has a second derivative with respect to r. Okay, so it looks kind of nasty, but those of you who are in Chem 131A know that there are certain advantages to switching from Cartesian coordinates to spherical polar when you want to talk about the solution of the, say, the hydrogen atom, electronic structure problem. Okay, so it looks like we're about out of time for today. So next time what we're going to do is we're going to see how we can use Mathematica's eigenvalue solution facilities to actually solve some interesting problems of organic chemistry or the electronic structure of conjugated organic molecules. So something to look forward to tomorrow.


Now the Senate has confirmed the appointment of Mosa Aliou as a substantive chairman of the independent corrupt practices and other related offences commissioned ICPC. On Wednesday, the President sent a letter to the Senate to request in the consideration and confirmation of nominees. Now, Dr. Mosa pledged to the Senate that the office will ensure to examine the system where there are gaps and to make efforts to minimize the impact of corruption. What we try to do in the ICPC under my leadership is that the most important thing which we need is the issue of proactiveness. We need to be proactive in issues pertaining to corruption. What we need to do is that we need to ensure that we examine some of our system where there are gaps. We try to block them so that they will minimize the incidences of corruption which will lead to certain things. In a similar development, the upper chamber also confirmed Professor Garji Dantata, Ibrahim Shekharau and Saka Boloji Suleiman as members of the Federal Judicial Service Commission. Of Mr. Mosa Aliyu, Adamu Aliyu for appointment as chairman of independent corrupt practices and other related offences commissioned ICPC. Those in favor say aye and those against say nay. The ayes have it. The nomination of Mr. Mosa Adamu Aliyu is thereby confirmed as chairman independent corrupt practices and other related offences commissioned ICPC. The nomination of Saka Boloji Suleiman is thereby confirmed as member of the Federal Judicial Service Commission. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


administration it will be facilitated by Jacob Green from the Osco Plus Plus network and as well I'm very sorry about the pronunciation of your last name but Mara I guess and just a quick word the Osco Plus Plus network is a global network and community of collaborative open source program offices they focus on supporting the commission objectives of universities government and civic institution and they have a great experience supporting the setting up of Ospos and they foster collaboration between them and build a co-collaboration infrastructures for today challenges yeah I hope you will all join us this afternoon for this as well and I wish you all a great lunch and as for our speakers of the day I'll invite you to follow Niaji to the outside also for a quick group picture and yeah that's all thank you all very much for your attention and enjoy the lunch


This is stock number 11538Z. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used heavy-duty truck headquarters. Today we are checking out this super clean 2019 Chevy Silverado 2500 crew cab short box LTZ. This vehicle has the 6.6 liter Duramax diesel with the L5P motor which pumps out 445 horsepower. This truck has been fully safe and inspected by our service shop has a fresh oil and filter change all the fluids Have been checked and topped off and this truck is 100% ready to go Black clear coat is the color we shoot all of our videos in 1080p 60 frames per second So if you have HD capabilities on your computer tablet or smartphone device Turn them on right now because it is definitely your best way to check out the quality and condition of the truck before seeing it in person And if you'd like to check out all the photos on this truck in the upper right hand party of screen is a link to our website Click that and check us out there. This one has the midnight edition, which gives you the painted 18-inch alloy rims and it has Goodyear Wrangler Dura-Track LT 275 70 R18 tires. These tires are like new on this truck I'd say Confidently 90% or more of the tread left has the Z71 off-road suspension package with the Rancho shocks Driver's side front fender is in excellent condition I didn't see any denser dings on there comes with the projector lamp headlamps the factory fog lights and the front bumper parking sensors No major denser dings on that front bumper. You get the chrome trimmed grille and the co-induction hood Hood is in pretty a nice condition Passenger's side front fender is in nice shape as well No denser dings on there and the passenger side front fender no scuffs or scrapes As you go down this side of the truck take note of how clean the body is how reflective and mirror like that paint is We take these HD videos So if you are far away or even if you're close by and you just cannot make the trip down But you're still interested in purchasing the vehicle You can see the truck hear the truck and have confidence in the vehicle that you're looking at Before you even get here so that when you do get here There's absolutely no surprises and that is why we offer the summit auto fast-pass option in the upper right hand part of your Screening link right to our website where you can apply for financing get pre-approved see a payment quote even appraise a trade Basically do your entire deal from home So when you get here all you have to do is drive the truck love it You'd be all set to go back tires are just as new as the front tires and the frame and underbody is in really nice shape Other than just a little bit of rust on the welds there But that's pretty common and the frame and underbody back under here is in great condition Has all the remaining factory exhaust so it hasn't been altered in any way and the lower rockers all look really good And it comes with the painted step bars Boxes in excellent shape coming around to the back rear bumpers in great condition as well No dense dings and that does have the backup parking sensors and the rear bumper steps Full towing package which includes a receiver hitch four pin and seven pin wiring The tailgate is in really nice condition as well, and it comes with a roll-up tonneau cover I don't see a brand on that, but it's in really nice shape Has the shock down assist tailgate And it comes with a spring and bed liner And it's one of those rolling tonneau covers that rolls up real nice Did you get LED bed lighting in the bed here as well and very nice and clean back here Tailgate shuts nice and solidly and as we go down the driver's side just as clean as that passenger side No dense or dings on the box And for full disclosure this back rim is in excellent shape as well Down the rest of the side the truck looks really good Didn't see any denser dings in the doors comes with the telescopic tow mirrors They fold in they telescope out And go in like so you get LED side lights built-in directional signals Inside the LTZ package gives you the black leather interior. There are no rips or tears on the seats They're in excellent condition Both these front seats are heated and cooled and you do get factory all-weather floor mats Auto headlamps turned out four-wheel drive factory brake controller tilt tilt and telescopic tome or telescopic steering wheel Power windows power locks power mirrors and these mirrors do power fold in I was like showing both sides such you know that both sides are working properly You do get memory driver seat there as well Pop inside the truck here turn the ignition on so you can see the miles and everything This one has 28,079 miles instrument cluster is very nice and clean notice you do get the Z71 Instrument cluster on there comes with the heated leather wrap steering wheel Bluetooth and information center controls on the right cruise controls on the left heated steering wheel control And then your forward collision warning is on there as well Six-speed Allison transmission with the optional tap shift and this one does have the Chevy my link system with the AM FM And serious XM radio capabilities. It also has the factory navigation system on it There's your AM FM and serious there Does have a CD player and you do get a projection manager on here where you can project your cell phone to the screen Via Android Auto or Apple CarPlay so if you've got a different navigation system on your phone You can project it to there and use that such as ways or Google Maps And then you get all your other apps on here as well.  That's for the cargo lamps I'm actually going to turn those on so you can show you those LED side lights parking sensors You can turn those off and on lane departure warning and then downhill assist control and that's your factory exhaust break down here You get two USBs two 12-volt power points and then a hundred Ten volt hundred fifty watt plug-in cell phone holder Passengers side floor mat and seat are in excellent condition as well There's no rips or tears on there and the headliner is an excellent shape too Does have map lights Home link buttons for your garage door security systems and lighting systems and then power sliding rear window button On-star capabilities in the rear view mirror And we'll check out the back seats and then Start it up and check out under the hood Back seats are just as clean as the front seats no rips or tears back here It does have the latch child safety system for any child car seats You may want to put back here power slide rear window with the built-in rear defrost Seats look really good and these do fold up for extra storage And you can see the carpeting and floor mats are in really nice condition back here, too Bottoms of the doors look good There are those LED side lights They're super bright Once again those turn on with the cargo lamps. We'll start it up and check out under the hood Starts right up No check engine lights or anything like that I would personally like to thank you for checking out the video today and hopefully from this HD video You've been able to tell just how clean this truck is all the way around Inside and out Under the hood we have a 6.6 liter Duramax season out by P-Motor 445 horsepower and space very clean runs very smooth Once again this truck has been fully safe and inspected by our service shop has a fresh oil and filter change All the fluids have been checked and topped off has like new tires on it and This one is 100% ready to go I would highly recommend it from a quality and condition standpoint and to see more pictures of this truck or one of Rather 450 new and used cars trucks SCVs mini vans Wranglers half tons the quarter tons one tons you name it We got to go to our website right there www.SummitAuto.com Full pictures and descriptions of every single vehicle through two locations all at Summit Auto.com And if you'd like to check out more HD videos You can go to youtube.com slash summit auto remember to like subscribe and share on this video and all the videos that you see there Back in a second. We'll see a link to subscribe to our YouTube channel in the upper left a link to more Chevy 2500 truck videos like this in the upper right a link to this vehicle on our website in the lower left and a link to our latest YouTube video in the lower right click those check us out and we're super excited to be offering this extremely clean 2019 Chevy Silverado 2500 Group Cab Short Box LTZ Z71 with the mid-edition package and black pickup Thanks again for checking out the video