In this video, we provide the solution to question number 13 from project exam number 2 for math 1050 We're given a three by three linear system three equation three unknowns. We have to solve this linear system We have to show all our steps What for which we can do this by substitution We can do this by elimination or we can use matrices that isn't do Gaussian elimination in general that last approach is actually going to be the most Effective the most accurate so that's the recommendation. I'm going to offer to you and that's what I'm going to present here if we write this in I should just say we write the system as a augmented matrix. We're going to get one negative two three draw your line seven And then we're going to get two one one and four and then negative three two Negative two and negative ten like so so looking at the one one position. I already have a one in that pivot position So that's great. So I'm going to utilize that to zero out everything below the one So I'm going to take row two and I'm going to replace it with row two minus two times row one and For row three, we're going to replace that with row three plus three times row one like so Now to help me avoid some arithmetic mistakes I'm going to take for the second row. I'm going to take the first one times of my negative two right as little super script So you get a negative two plus four Minus six in that situation and then minus 14 and then for the last row We're going to take the first row in times of my three. So we're going to get three minus six We're going to get plus nine You don't have to write the plus if you don't want to but the minus signs are pretty critical there And then you're going to get 21 right there So then we do do these row replacements Like so the first row stays the same nothing changed one negative two three and seven Just just copy it down the second third row of course will change you're going to get a zero below the one one plus four is five one minus six Is a negative five and then four minus fourteen is a negative ten right? I can see in that row I already have everything divisible by five so without even doing the third row I know my next thing I'm going to do is I'm going to take row two and I'm going to divide everything by five We'll get to back to that in a second. So then we get zero here negative three plus three Next we're going to get two minus six, which is negative four. We're going to get negative two plus In that case that was a nine I didn't I didn't write that very well, but you're going to get a seven Right there and then lastly twenty one take away ten is eleven like so So yeah, I'm sticking with what I'm what I said before my new pivot position is going to move to the two-two spot I would love a one there if I divide by five that'll give me exactly that so just copy down Your matrix again This time the second row becomes zero one negative one and negative two then zero negative four seven and eleven like so For which then with my pivot position still right here. We are going to take the We're going to take the third row and we're going to replace it with row three This time plus four row two if you want to you could take out this two right here right now That seems fine. Let's just do it We're going to take row one and replace it with two times row two like so We want to get zeros other than the one there So if we take row two and times it by two, we're going to get a two We're going to get a negative two and we're going to get a negative four Then in the bottom We're going to get a plus four We're going to get a minus four and then a minus eight like so. So then what is the next? Equivalent matrix here. We're going to get one zero one and three Row two didn't change so we have one negative one negative two and then last we get zero zero Three and then eleven take away eight is likewise going to be three right like so so again that worked out pretty nicely for us I'm going to divide row three by three itself This then gives us our next matrix Because after all our pivot moves now to the three three position there So if we divide by three we still get one zero one and three We're going to get zero one negative one and negative two and then last so we get zero zero one one And so using this final pivot, let's get rid of all the other entries here So in the second row, we're going to take row two just add to it row three and then for row one We're going to take row one minus row three like so. So we're going to add one add one We're gonna minus one minus one and then that should put us in our row reduced echelon form for which We get one zero zero two The next row we get zero one zero negative one and we get zero zero one one And so then we can record our final answer here that XY and Z are equal to Two negative one and one the final solution for which we did this using Gaussian elimination. Like I said, you could have also used some of the other techniques we developed in this class But I think this one works out pretty nicely in the end


How's it going everyone at Caleb here with late and sports cards next up tonight? We've got another box of the Almanac sports card multi sport edition here. This is the personal's edition volume number two Box 21 that is for David G. Thank you very much David. Good luck here Yeah, we're cranky whoops we are cranking through these here we go.  Oh my goodness. That's so cool That is just something you don't see man David G. How about that for the collection?  Yeah, that is That is great Pieces of authentic game used memorabilia Congratulations, man So awesome David So awesome heck. Yes Well get that right out to me and thank you again David great card man


Okay, so three years, five buds, and now we have the Galaxy Buds 2. Let's see how they stack up against the other buds. So let's jump in. Yes, the Galaxy Buds 2 are here and I have been checking them out for a while here on the channel. So you guys will know which is the best Galaxy Bud to pick up. Now, if you're watching this for the very first time, go ahead and smash that subscribe button and the notification bell to get notified for more videos like this on the channel. So the Galaxy Buds 2 come in at a price range of $149 and they are the latest Galaxy Buds you can get. They've got that similar, you know, square with rounded corners case with USB Type-C charging. You've got wireless charging built into them. You know, all the fun stuff that you found with every single Galaxy Buds here. But once you open it up, it reveals a very different color scheme within the cases. Now, the case is similar to the Galaxy Buds Pro in live. This one knows different with the white background for all the cases, but the different colors to match inside. So I've got the green color here. Sound, of course, is tuned by AKG and the buds look very, very different. One of the things I do like about them is that once you open them up next to your Galaxy device, they pair instantly. It's a very quick process. Now, the other ones in the past did a good job, but this is just much faster and you are good to go with your Galaxy Buds. Now, in terms of just the size, they are much lighter in size compared to what you had with the Buds Pro or even the Buds Plus or the original Buds. Very light, they're comfortable, and I'm so happy they've gone back to the traditional ear tips as opposed to the much bigger rounded ear tips you found on your Galaxy Buds Pro. Now, speaking of the other Buds here, let's just go back a little bit on memory lane. 2019 Samsung should use the Galaxy Buds themselves. They've got that pill-like shape, it's got a really comfortable fit, and they looked really nice and they give us some good sound at the time. Now, the one thing you notice with all the different Galaxy Buds is that the app is slightly different for each one. So with the Galaxy Buds themselves, you do have some functionality that is only for that and some functionality that extends forward. Now, moving forward, we have the Galaxy Buds Plus. Now, the Buds Plus brought in better microphone quality and also a longer battery life. And again, keeping that same fit and feel and honestly, it has one of the best fits while using your Galaxy Buds there. And again, as I mentioned, the app is different with more functionality and a different layout altogether. Now, we come to the one that a lot of people don't like and I see Daniel there making faces. I'm talking about the Galaxy Buds Live. The Live have that bean-shaped look, they've got the new case design, and they fit really well and comfortable. They supposed to have active noise cancellation, but honestly, I couldn't really hear it or experience it, but they did give us some good sound and a much improved microphone. And again, as I mentioned, the app looks slightly different. Still the same Gear App all the way through. Speaking of Gear App, who remembers the Gear 360 camera from Samsung, just bring that out. But anyway, this app has been on for a while and I'm glad to see that Samsung keeps improving it for all the different devices. And then we have the Galaxy Buds Pro, which launched with the S21 Ultra that brought in so many features you can see on the app, like of course, the 360 audio, active noise cancellation, speak to chat, so many more functionality that you won't find in any other Galaxy Buds and it's represented here. Now, this is one where people have mixed feelings because the air tips just didn't have that perfect fit. Now, that brings us to the Galaxy Buds 2. Now, Samsung here used this device to fix some of the issues they had across the line. So in terms of fit and comfort, I would say this is the most comfortable Buds you will find out of all of them, all five here. They're very light, they're very comfortable and they fit quite snug. So that part is comfortable. Now, when it comes to the application use, it's similar to that but right now the app has less features than even the Galaxy Buds Pro. Now, the Buds Pro has, of course, that 360 audio speak to chat, you don't have them with the Galaxy Buds 2. Now, the other thing also with this is talking about sound. That's one of the most important things. How well do they sound? And how well do they sound compared to the rest here? I really love the audio I'm getting from this. It sounds really nice, the highs are strong, the mids are good, a bit softer for me and the lows are, aka the bass is really not that much but I'm not a big bass fan and if you like more a lot of bass, this might not be the best for you. Yes, you can use the EQ app for it but the Buds Pro kind of lean more to that direction. But in terms of audio, I think it's really on par with the Buds Pro. I'd say the Buds Pro just slightly ahead. Now, the other thing, of course, is active noise cancellation. So when I'm in the city, walked around, got on the train, used them and I've got to say they're pretty much on par with the Buds Pro. The same. Because also the fit is much better, I think for me it felt a little bit better but I think in general you're getting probably one of the best active noise cancellation you'll find in earbuds, at least comparable to other manufacturers as well as also what the Buds Pro bring to the table. So when it comes to microphones, that is something very important and the Galaxy Buds 2 have done a really good job improving from where we started off with the Galaxy Buds, Buds Plus, Buds Live and even matching or sometimes I think even slightly better than the Galaxy Buds Pro. Now, when I've had conversations with friends, they've all said, look, it's been clear and crisp. I couldn't tell them what Buds I was using but they were like, look, it's like you're on your phone. So that of course is a very good sign and I think when it comes to microphones, the Buds 2 do a fantastic job. I forgot to also mention you do have transparency mode and you've got three levels on it on the Galaxy Buds 2 and they're really good. They sound really good. You can have the buds in your ear comfortably, you can hear everything around you, play your music and it's a very good feel. Now the question at the end of the day is, which should you buy? And I think it's simple and slightly difficult question because when you look at the pricing, it's a bit all over the place. The buds are kind of refurbished right now so of course that's about $79, maybe $69, Buds Plus you can find them for $99 or $79. This Buds Live 129 while the Galaxy Buds Pro are recently priced at $169 instead of $199 and the Galaxy Buds 2 are priced in at $149. So if you're looking for a better fit, you're looking for great audio, great microphone, and solid active noise cancellation, this is the pair of two others Buds from Samsung to pick up. Now if you want a little bit extra like the Speak to Tat 360 audio, those auto little extras, then the Galaxy Buds Pro will do that for you but remember the fit is something that can be a little bit difficult. So for me in this video, I got to go with the Galaxy Buds 2. I think this is the refinement Samsung's needed and again with all devices it usually takes three years to get that fine tuning right and I think they've got it here and as always Samsung always updates the application and the software so they tend to improve the sound and some of the functionalities you will find. Hopefully that gives you guys a good idea of the Galaxy Buds 2 and what to expect. If you liked this video, leave your thoughts down below. Let me know which you're picking up if you want to pick up the Galaxy Buds 2. I have a link for you down as well as the other devices you see on here. Otherwise, don't forget to like, share, subscribe, check out my next video on the Galaxy Z Fold 3 and always enjoy your entertainment.


In a deep survey for small, faint objects in the Orion Nebula, astronomers use the Hubble Space Telescope to uncover the largest known population of brown dwarfs sprinkled among the newborn stars. In the process, they also found some very massive planets. Here are some of the combinations they found. These are brown dwarfs orbiting stars. Here's a planet orbiting a brown dwarf. Here's a brown dwarf orbiting another brown dwarf. And here we see two giant planets orbiting each other without a star. Surveys like these indicate that brown dwarfs may be among the most common objects in our Milky Way galaxy.


My name's Tim Taylor. I operate Crossroad Farm in Post Mills, Vermont. And I farm approximately 50 acres of mixed vegetables. We have greenhouse tomatoes. We grow approximately 15,000, 16,000 pounds of those. Quite a big bedding plant business now. And in the field crops out here, we grow just about everything. One time we even tried artichokes one year. We have, as far as weed strategies, I think probably the one I focus on the most is to keep my corn crop the cleanest I can. I use that as a way to come into my next fields because in my operation it takes up a great deal of the acreage. I like to let no weeds go to seed there. But we use no herbicide there. I want to stress that right from the start. We never have. I've always cultivated it. I use a single-row cultivator. I use a two-row cultivator, the rolling Lilliston-type cultivators. And I use some blind cultivation with rotary hose. This is a rotary hoe, which we use in corn. It comes in all different lengths. This is actually a very small one. It's been cut down, so it does two rows of corn. We use it for blind cultivation. After we've sowed the corn approximately anywhere from four to five to perhaps a week to ten days later, depending upon the soil temperature and the time of the year, we'll come in and we just run this right across the top of the crop blindly. This is usually pre-emergent or just as it's spiking up. I use this in corn. I've used it in peas and in beans. It will get about approximately 50 to 60% of the weeds. It will get approximately, oh, maybe 2 to 3% of the corn, or the crop you're trying to actually grow. Depending upon your timing, you can actually come in when the crop is not so much corn, but peas and beans when the crop is actually up and starting to leaf out. It's one of the pros and the cons of this. It allows you a little more time for more finer cultivation because it does reduce the pressure, the weed pressure for a period of time, and yet it doesn't get them all and you still need to do cultivation. I find I still need to do single-row cultivation as well. Each sprocket here is spring-loaded. It'll bear the full weight of the unit. You can get a little nervous sometimes when you use it because it does sink into the ground quite a ways. I find that I'm quite safe as long as I keep my corn planted at 2-inch level. Corn planted up a little in the 1-inch zone will tend to be dug up a little more often. One of the problems with this tool is that it picks up all my loose plastic from my crops like melons and zucchini and squash. I don't know if it's exactly a down size. It gets it out of the field, which I do want to get it out. The other primary cultivation tool I use is a slightly modern version of 2-inch shovels. We call these the curb-co bat wings and their first single-row cultivation, although I have seen them used in other applications in 2- and 3- and 4-row cultivation. What they consist of is a series of old carb bumpers that have been fashioned into these bat wings for throwing dirt. Some of the things I really like about it are if I have some very mature weeds and come in quite late, it cuts under them and cuts them quite effectively and rips them up. It's quite effective where I do have some witch grass because again it rips it up. Here we have the budding basket weeder and what we do here is we plant, all our lettuce is grown from, is transplanted. We do nothing from seed into the field. It's all transplanted and it's a 2-row bed system. A week after transplanting approximately, we'll come in with the budding basket here, which is ground-driven off of this chain here. We can go approximately just about as fast as you'd want to drive it on the open field, 5 miles an hour or so. It's advantage is that it won't throw dirt into the lettuce. It moves in this manner and kicks up the weed seeds, cultivating at about 1 inch depending upon where I set it in the ground. We wait about a week because we get a little bit of germination, but we don't want to wait too long because we don't want the weeds to be too big. The advantage of the belly mount is that it does not wander. The cultivating tool doesn't wander in the field as it would behind the tractor but this place behind the tractor. I'm able to view straight down at the single row. I can't see both rows but I can see one row and I just can see exactly where I'm placing the tool. Absolutely exactly. If I daydream a little bit and it wanders off, I can catch it real quick whereas when it's behind me, in the case of some of the 3-point hitch tools that I use for cultivation, it tends to wander a little more and I cannot have quite the same control that I would have. I want to stress this. I own two of these Kubotas and this is mounted here all year long. I don't take this off. It's not difficult to mount. It just has four bolts here and four bolts on the other side but I have it set just perfectly the way I want it and I honestly believe you should have a tractor for each piece of cultivating equipment you have because the downside on all cultivation is the setup time. What we do is the basket is spaced six inches apart and I'll do two passes here. The first pass I'll be nursed right up next to the radishes down one side. I'll turn around and come back in the same bed up against the other side as close as I can go and that way I get within usually an inch to two inches of the crop even though I have six inch spacing on the basket. Here's the perfect field cultivator. This is something new for me that I'm just experimenting this year with. I hope it's going to reduce my reliance upon a motivator in my field bed preparation. Normally what my present practice is to subsoil in the spring, put the subsoil on a two shank subsoiler, run around the entire 30, 40 acre farm subsoiling. And then gradually manure and motivate and make beds as I need them. And then in the fall once again use the motivator to incorporate the residue. And I have some concerns about soil structure and I'm trying to look for alternatives to that especially the bed preparation in the spring and also again for witch grass control.