Welcome to the second interview talk. The topic today is BIM, Building Information Modeling, Digitalization of a huge industry, good prospects for future and society. I'm Denise, I'm your host together with my colleagues from Team Interview. We will lead you into different focus topics until this year's interview event in September, hybrid. So, well, Building Information Modeling or consistent information management in planning, construction and existing buildings is extremely important topic. Digitalization in the construction industry is lagging miles behind other industries and the construction sector is associated with a lack of efficiency and sustainability. But more important, the issue of enormous social relevance. If you look at the ecological footprint of the construction industry as a whole, one is shocked by the extent of the waste of resources and the climate impact of the construction industry. And you an environment program called Global Status Report for Buildings and Constructions from 2020 comes to a devastating conclusion. Nearly 40% of global CO2 emissions are associated with the construction sector, 40%. And then there's the issue of waste. In Germany, the construction industry as a large sector of the economy is responsible for half of all waste and recycling of materials is absolutely below average. But from the other side, however, it also means that there is enormous potential for saving energy and materials in this construction sector. So, and there are plenty of opportunities for optimization in term of efficiency, cost savings and sustainability. So, this was my introduction and we say right now, let's talk. We are pleased that we have been able to attract BIM experts and real BIM fans for this intergeotalk. So, our experts for today are Emmanuel Di Giacomo. He works more than 30 years in the architecture, engineering and construction industry. For Autodesk, he is the AEC ecosystem manager for the region Europe, Middle East and Africa. He ensures that the industry is embracing BIM and expanding its ecosystem as widely as possible. He is responsible for the new digital approach to the reconstruction of Paris Notre Dame Cathedral, which was destroyed in 2019. And with us is BIM expert Ilka Mai. With her company, Locklap Consulting, she offers digital twins for almost every application. She is a tireless fighter for digital methods in construction and expert on digital twins. For almost two decades, the doctor of geography, Gis and BIM expert has been working with spatial data and technologies. Until 2017, she worked for the international engineering firm Arab in the UK. She led the development of the step-by-step plan, digital design and construction, was deputy head of the UBIM task group and accompanied the BIM strategy of Deutsche Bahn. Our third guest is Ulrich Hartmann. Ulrich Hartmann is working as product manager, common data environment expert and BIM expert in the Oracle Aconex strategy team. He is enthusiastic about digital methods for the construction industry since his studies of civil engineering and computer science at the technical university of Berlin. Various stations in digital fields of product management, research and software development give him a practical background and expertise. As part of the international product strategy team, he fights for innovative digital solutions and the implementation of the BIM strategy in product roadmaps. So first of all, thank you for joining us. And each of the guests starts right now away with this short lecture on impulse. Then there is a round of short interviews. We have about two or three questions. But what is very important, please ask your questions in the chat at any time. So and right now, it starts with Ulrich Hartmann and his impulse to, I hope I say it right, Ulrich, please correct me. I would say, you say something like BIM is the application to make the construction industry more sustainable. But the stage is right now yours, Ulrich. I hope it works perfect. Thank you. So welcome everybody. Thank you, Denise, for this nice introduction. I just want to, of course, also welcome to the audience. I want to start with three BIM statements at the beginning. First statement is BIM is just more, much more than just nice 3D visualizations. It's about the non-visual contents inside our information models. And models are, of course, I would say, made for a purpose. And they require information and these requirements need to be explicitly being specified by those who need this information. Second statement is BIM is about information management. That does mean actually we are producing information collaboratively in a distributed way. And these pieces of information have to be put together in a managed process with quality checks in between so that everything, every information fits together at the end nicely and people can consume those information according to their purposes. So if we look at this nice little picture on the right, we see people sitting together and trying to get to feed themselves. But this fails because they use improper tools. There's lack or losses of soup in this case, but if you transfer this metaphor into information management, it's also lack of information. So some people come then to the conclusion it's better to collaborate in a nice way and feed each other, give each other the information they need. So that's kind of a cultural change we also imply with the application of BIM. I found this nice analogy. And the third point is about integration BIM is not standing alone. There is a world around us that does mean we build us off residential commercial, industrial buildings and so on. We interfere and interact with systems like energy, supplies, telecoms, with a natural environment, of course, and social infrastructure, transportation systems around us. And as you mentioned, Denise, in the introduction, we produce a lot of ways and we take some resources out of our natural environment. So that's a lot of interference we do in construction. So this word or this upcoming hype, at least about digital twins is shaping out the interaction between what we do and what the rest of the world is doing in terms of digital. So this was the three statements at the beginning. How do we at Oracle Equinix live up with our own expectations and visions? First point is we are very active in the development of standards on several levels on ISOCEN, European, German, national level. Second is in the Building Smart International community, where we work out and shape out or help shape out the new prestandards. You all know the industry foundation classes coming from Building Smart International and further standards will come up. We published a positioning paper about ecosystems of digital twins last year. So if you want to download this from the Building Smart International pages, and the last statement I would make here is we also have to prove our own software against being compliant with standards with open web standards. And the last achievement we made here, we earned this BIM Swarm German certification saying our software is compliant with current BIM standards. So this was my five cents on this. Hopefully in time, I have to show the state power statement at the end for legal reasons. This is just saying if I'm talking nonsense here, please don't blame it on Oracle, just blame it on me. That's what it's saying. So thank you for your attention. That's it over to you, Denise. Yeah, thank you very much for this short lecture for giving us these insights. Dear Ulrich, and yeah, you as you just mentioned, BIM models are made for purpose. And yeah, your commitment to these standards belongs to the standard. So could you just briefly explain the meaning of these standards in a context for us? I mean, it's one side of the same. I'm making standards or helping make standards, which is quite an exciting thing sometimes, because there is sometimes a collision of interest and much fighting for the best standard best solutions. But there's also a famous saying from one of the Siemens, he said, standards who makes the standard is owning the market. That does mean there's a huge of commercial interest. So this is actually a market enabler, standards are market enabler. And this is true for if you travel through through the UK, for example, you won't get your charging device into the wall outlet because it's different pins on your plug. So the same is with BIM standards. Information does not fit together. People cannot work. As this picture I showed the set, it's very important to have standard that that's where the excitement comes from, from my side, to enable the market. What do you think about the pace of action in Germany? Is it slow? So where is Germany when it comes to BIM? Yeah, the pity is I'm looking always at the UK and I'm very let's say jealous about how would they approach and how do they proceed? And we are significantly lagging behind Germany. That's a pity. We have this nice step by step plan and still are on the step one for years. So it's necessary to speed up to not lag behind in the international compared what others do. I guess or I just read in an article, you compared the digitalization in the construction industry with a pandemic management. So why do you set this? And what do you think needs to be done?  This article is not from my company I'm working for. So just to be careful on this, but I see some parallels in the handling of the pandemic in Germany with how we approach BIM in Germany. I mean, if you look at our health care system and the health authorities, how do they work in Germany? Paper and pencil and phone calls. And this is not very digital, to say the least. So if you look at our building authorities in Germany, you will see the same things. They are under equipped. They are under trained. They are under funded. And we are on one half on this step by step plan, and developing electronic building permits. This is all done. I mean, there is no problem with technology. There's a problem with administration and funding and making administration fit for BIM. Ulrich, you just mentioned that you look to the UK when it comes to standards and BIM and the PACE. And Ilka is with us today. And till 2017, she worked there in the international engineering firm Arup for the UK. Is that right, Ilka? And maybe, yeah, I mean, your topic is related to the statements from Ulrich. You also say there's a lack of standards for BIM and existing buildings and existing structures. And you also meant that not everything that is possible makes sense. So would you explain that? And welcome Ilka Mai from LogLab Consulting. Hello. Thank you. Thanks, Denise. Yes. So what I would like to talk about is now BIM models for existing assets, not only building those types of assets. And Ulrich just mentioned the term digital twin. And in my experience, there seems to be a bit of a confusion between what is a BIM model and what is a digital twin. This is the same, this is different. If we could just look at the output of the BIM process, as Ulrich described it, it's an object-based 3D model representing an asset that doesn't exist yet, because usually BIM describes the design process of something that doesn't exist yet. If we think of a digital twin as an intelligent and digital representation of existing assets, which enables mapping of objects to other data sources and optimizing processes, et cetera, then we see there is a big overlap in the sense that we're talking about a digital representation, that is object-based and has a certain structure. And now a lot of people see that a digital twin not necessarily needs to have a spatial representation of the object. However, we in LogLab, we believe that without the U2W, if you do have a three dimensional digital twin. And therefore, a BIM model has the output of the design process and a digital twin has an output of a copy of an existing asset. It's actually quite similar. However, the way how we get there should be different. And that's also why I'm saying there is a lack of standards. Just picking up on a couple of things you mentioned earlier, the needs of sustainability and ways, et cetera. So when we look at existing assets and the challenges around existing assets and we look at the asset managers, we see that they have a lot of problems and challenges around them. So very often they have to manage a large portfolio of assets. They could be all around the world, production sites, et cetera. And they are under immense pressure to save carbon and save costs, looking at the whole life cycle of the assets. They very often also have a historically growing environment of IT systems and data systems and data. And that means that very often they can't really access the data quickly. They can't make good decisions based on good data quality. They don't know what the quality of the data is. It's outdated, et cetera. But lots of challenges around data. And when it comes to then maybe refurbishing parts of, let's say, a railway station or something, then very often we want to start the new design in BIM and in 3D, but we're lacking the 3D data and the 3D models to do that. And that all together creates a need for better information around existing assets. So when we now think of these models and the data, I think we should agree that we need four ingredients and components, which we really need to make this solution scalable and that technology really adding value. So first of all, as we said, we need objects. Just the point cloud or mesh is not really adding value. Usability in terms of trial sizes, for example, runability, how can I operate that? What do I need? And creating a pair of bytes of data is also not helping. The next one is the valid business case. So if you make these copies, these digital twins too expensive, then it won't fly because you won't have a business case. And also if you add another file of information that doesn't help, then you should look at the digital twin as a proper data integration solution. And if you put all these four ingredients together, then I have a very strong case. We can talk about layers of scanners in this context later. They produce highly accurate data, but not object based. Therefore, it needs a bit of thing, a photo thing after the data capturing. And a lot of people think the struggle is how to specify the output that they want to get out of the data capturing process. And then when we talk about the models as an output of the design process of the model, then a lot of people now seem to get their head around how we use them in the design process. And then they try to apply the same method and the same standard for copying existing assets. That is not helpful. It creates, it's too expensive. It's too labor intensive. And it doesn't necessarily create a good result. So when you look at this old structure that we see in the picture, and this is from a real case where a team was given a point route and asked to model this structure using a graphic dim tool. And then they looked at the results and they found the results were not good. Because these retaining walls, they were quite deformed from age and from the pressure coming from one side. But a design tool will always assume that a wall is straight because we don't design dented and buckled and deformed walls normally. And there's a lot of problems that you can get into when you use the wrong tool. As Uli just mentioned, the wrong spoon to eat the food, then it just doesn't work. Yes, but there are ways how we can produce these object-based models from, let's say, non-photographs or videos and create object-based digital twins for the different purposes and different uses. And as Uli said, models are made for purpose. To understand your purpose is really important. And then find out what the best way is to get there. And then we will have another business paper here about my short birth of introduction. Thank you. Wow. At this point, I would also like to address to the audience, if you have questions, please ask them in our chat because our experts, we will start with a panel discussion soon and our experts will answer your questions. So if you have questions, post them in the chat. Ika, according to your comments or just your statements or lecture you gave, BIM is not a general tool for planning in existing buildings. You also said that the design is not to rebuild the real environment outside. So where are the limits of the method? I see it's simply the cost and the scalability. But if you think of the huge amount of existing assets that we operate and they are sometimes very old, they are 100 years old or 50 years old. We are lacking good data of these assets to operate them more efficiently and to know how do we need to look after them. When you then think of the design process, the design process needs highly educated and experienced people, architect engineers and they use sophisticated tools for the design process. Now, there must be a better way of creating a good information model of an existing asset and not pretending that we were starting it from scratch in a design process. That is not the right way to do it. I think what we need to get better at is to specify the quality of the output that people need to operate the assets and not use the design standard and the design tools to do that. The scalability that is putting the break in here. Okay, yeah. So we can do a lot of existing structures, existing areas, constructions. Yeah, definitely. I mean, when you just think of, you want to understand where information is to start with and that is where a digital twin, as we showed it earlier, object-based 3D representation is a very intuitive way to understand how you get to information, what information do you want. So let's say you're managing a building and you have a dashboard and the dashboard contains a lot of values of sensors and room, et cetera. And you see that as the line has been triggered in one of the rooms, what you see is a long list of numbers, but you don't get the context. You don't know where that is. If you have a digital representation, a facial representation, where you can see, oh, this alarm is triggered in this room, so you can, in the virtual room, you can walk into the room, you can look inside, you can look in the room next door, and you get the full context, then you can make a much better decision. That's just one example in their hand. Interesting. So what do you think needs to happen to advance this use of BIM in planning or in these existing structures or buildings? We get better to understand the requirements and also then in the procurement process how to specify that when a company procures the data about the existing assets. Because at the moment, a lot of companies are using the design standard to procure data about existing assets. And that's why I'm saying this is too expensive and they're forcing us into a way of working, which I don't think at value. So for example, you might have heard of LOD. LOD is now a term, level of development, how you specify the quality of information. And it's a term that's been developed for the design process because it specifies the maturity of the design. And you can specify in terms of the geometry, the maturity and the level of granularity for the geometry, but also then for the information that is attached to the object. Whereas from an existing building, there is no level of maturity. That's the only thing that exists there. So people need to get better at specifying the actual data that they want. What position accuracy do they need? Do they need to know by the millimeter where a switch is or could that be just a centimeter off and it doesn't matter? What granularity of objects do they need? What is the object based on structure? Do they need level one, level two, which level does it go down? Because what information do they want to have attached to the object? And that's where I see a big lack of expertise in understanding the actual data that people need to operate with the asset better and then therefore start procuring exactly the information. At the moment they're over specifying and they're spending far too much money on procuring the right data. Thank you very much Ilka. If anybody is interested to go deeper in that talk with Ilka, we can also ask your questions at any time and we will right now continue with our third guest, Emmanuel Di Giacomo. I'm very happy that you also found your way here into our virtual roundtable of this interview talk about BIM. Your statement is a kind of, I say with digital methods, the Notre Dame Cathedral will be rebuilt in half the time as in the traditional way and the effort pays off twice. Notre Dame may be equipped with sensor technology after the reconstruction, so a similar event that tragedy would unlikely to happen again. That sounds very good. Please explain this to us and the stage is now yours. So as you were mentioning, yes, we know that thanks to BIM, we think that we will be able to reconstruct Notre Dame faster than in a very traditional way. So I'm working on this project together with a big team and when the cathedral took fire in 2019, we straight away thought that we would like to help. So first of all, we made a cash donation and we straight away got in touch with the organization, the public organization in charge of the reconstruction and the President Macron wanted this to happen in a very fast and efficient way and this is why he named the general of the Army that you can see on the left, the general Charger. And one way also to help for us was to, we considered that in terms of heritage, we would be able to help fasten the process using the BIM and using pushing the limits of BIM actually to make this process more efficient. So we work together with some experts in order to create an existing model before the fire of Notre Dame. You have to be aware of the fact that Notre Dame didn't have lots of documentation available, which is really a pity actually. And the first step was to go from a scan to BIM process and this is what was achieved using this as you can see on the screen, this kind of point cloud model. This is a view from the top and there were thousands, it represents 46 thousand millions of pixels of data. So there were both data coming from laser scanning operations as well as the drones, drones were used in order to get the aspects of the cathedral. So part of this point clouds, by the way, were coming from previous campaigns that was done with famous archaeology, especially called Andrew Talon. And as you can see from the top of this presentation, we had to work with many point clouds files. We had to clean them to analyze them in order to see if there were any problems on the existing model. And then we recreated a BIM model that you can see under this. We chose, so Ilka was mentioning LOD. We chose to work on the LOD of 300 and here you can see from the left to the right, so the point cloud survey. And then you can see the point cloud with the BIM model of Notre-Dame as well as the final version of the BIM model. As you can see, it resulted in a very high fidelity model for the design in a rabbit, obviously. And this was very important because all the people, all the companies that are involved in the reconstruction process of Notre-Dame didn't have any material in order to plan different values, aspects of the future reconstruction of Notre-Dame. And also you have to take into account the fact that for almost one year since last year, there was all the scaffolding on top of Notre-Dame which was melted. So there were many operations before that had to be processed in order to remove, for example, the scaffolding and there were some security operations around Notre-Dame. Also, we not only remodeled Notre-Dame itself as a cathedral, but we remodeled as well the presbyter, the presbyterysary, also the crypt and all the surroundings of Notre-Dame to be able to facilitate the future operations and logistics on the sites. And this is where also BIM is very important. This is a version of the resulting BIM model, which is more of a structural model. We have an accuracy, look how I was speaking about the accuracy. We know that we have an accuracy of between one to four centimeter, which is based on the point cloud, of course. And thanks to that, and again, we are talking about the importance of data. Thanks to that, all the reconstruction team is able to evaluate, for example, the number of cube meters of stone walls or the zinc roofing, the number of walls on such a very complex and this is where the challenge is because on a typical building, modern building, it's not a very big challenge, you know, to model a building with such a monument, a historical monument. It's very difficult because here we have 186 boats, which are all different. And why did we show, did we choose out of the fact that we are convinced that BIM is important for and BIM is digital and digital are important for the construction industry. We are also convinced that it brings value to the multiple reconstruction teams that were consigned because it's about 250 companies that are working on site. So here, sorry normally there is an animation, but yes, sorry, just going here. We know that it will help in the values phases of reconstruction. For example, we know that our technology could help in order to explain the complex structural geometry to the values traits that are involved on site. It could help to extract any kind of 2D documentation or the production of this documentation. We will be able also to reconstruct, to define the reconstruction planning and phasing. Eventually the architects in charge of the historical monuments could also eventually design the roofing of Notre Dame. And also very important part of this reconstruction process is around the systems routing because obviously everything has burned, so they will have to redesign everything. And it will help in the security aspects also on site for the workers and staff security, obviously. At the end of the day, as it's a very complex process and as the French president defined that it should be rebuilt in five years, we know that thanks to being this could definitely help. As also Ylka was mentioning, it's very important to define the business cases and the use case. If you're able to at least reach two or three or four objectives, I mean, you will be sure that you will have a good return on investment. And in that case, we define together with the reconstruction team that we will be using beam for the reconstruction, planning and phasing, which is about the fourth dimension, which is about time, and the fifth dimension, which is about managing quantities, kind of information also. It will be very helpful also for the site installation and logistics management in order to be sure that everything like cranes will be positioned correctly, that we will be able to bring the materials, the trucks, et cetera, at the right place on the site. And finally, very important, we want to make sure that the collaboration between all the thousands of stakeholders will be efficient with the collaboration platform like BIM 360, that you can see on this screen. And also, we speak a lot about collaboration nowadays, especially with BIM. The collaboration is really critical to the success and time savings. And the time savings are the key in these kinds of huge construction sites. So as a conclusion, I would say that here in that case, which is a very specific case, BIM will help to build faster, better, with less resources, obviously. And it will help protect our heritage in the future. And that would terminate also with so you can really mention the importance of digital twins, which we definitely agree upon. And we are definitely convinced together with the owners of Notre Dame that having a digital twin model of the cathedral with the right information, the right level of detail, right level of information connected with IoT sensors will help in the future to correctly operate and maintain these kinds of monuments and avoid disasters like the one that this cathedral has been suffering from. So thank you very much. Thank you very much for this presentation of a project that has made waves all over the world. I mean, everybody remembers the pictures in the news or the social medias from Notre Dame Cathedral when it was burning and burned down. So thank you very much for these insights in the construction and the building. And yeah, you decided with your team, with your know how to recapture the cathedral. So why did you decide to recapture it? Because first of all, as I was mentioning, there was no documentation available at that time. And together with the team in charge of the reconstruction of Notre Dame, we really had to analyze the differences before the fire and after the fire, first of all, in order to understand if there were any disasters, the cathedral that may be moved, et cetera. And then after, we thought straight away about the roofing system and the carpentry. And we had to think about and brainstorm around the possible redesign of the roofing. And you know that there have been lots of discussions also around the world. So we had to have something concrete, a 3D model with information which would have helped to take better decisions and not make any mistake in the reconstruction of Notre Dame. So this was obvious that BIM was the right approach. OK. So but right now you have much better tools. Just describe once again your tools you use right now. So the tools that are currently being used on Notre Dame, so first of all, for all the point clouds, there is RECAP, RECAP which is a software which allows you to load and merge different point clouds coming from different sources like drones or laser scanings, etc. which allows you to do some analysis. Revit has been mainly used for the remodeling of the cathedral. So Revit is one of the most famous software in the world, BIM software in the world. It's a pre-disciplinary tool. And we are at the core of the collaboration process. There is BIM 360, our collaboration platform. And we've been also making some tests with our digital twin solution called TAMBEM. Thank you very much for the explaining these BIM methods to me. And also the question to our audience about 80 or 90 participants are with us. Do you have questions to Emmanuel about the reconstruction of the Notre Dame Cathedral to concerning the BIM methods used? Just ask them right now in the chat and we will answer them right now. So right now I would like to continue with the panel, the whole panel with Ulrich Hartmann, Ilka Maip and of course Emmanuel Di Giacomo. Yeah, we just heard about the BIM methods and well just one more question to Emmanuel. So the reconstruction of the Notre Dame Cathedral is absolutely extraordinary. I mean once in a lifetime project, is it? Yes, because as you know Notre Dame was born something like hundreds of centuries before, you know. So it's a very it has taken lots of hundreds of years, you know, to build this cathedral. And it's one of the hugest cathedral in the world. It's an iconic monument and it's amazing to be working on this monument and to be using modern and innovative methods of construction and in that case reconstruction. So we are very honored that it's a challenge for us which also helps us, you know, to bring some evolutions to our technologies, of course, because this is totally different from using BIM technology to with modern buildings. Ilka Ulrich, do you have any questions to Emmanuel or in the other way or should we just start with our all-together discussion right now? Shaking your hand, perfect. So, yeah. Yeah, yes, yeah. But immediately comes to my mind is Notre Dame is a landmark object, project, whatever. And you mentioned Emmanuel, there's nothing you know about this in terms of how it's being constructed, the material inside and so. And isn't it that we have many, many small Notre Dames in our cities? So we actually do not know what's has been built in. If you look at the Grenfell event, for example, we even do not know about dangers in materials we have built in. What do you think? I mean, Ilka mentioned it's a huge effort to digitalize each and everything. So that's not the way we can do it. But how do you think we can proceed in this regard? I think that so you are right. And there is not a single recipe, you know, to understand how to collect all the information, which is very different because we realize with this kind of project that any kind of information is important. A piece of paper, some photographs and there has been in the context of Notre Dame. So it was not managed by us, but there has been a huge campaign of retrieving all the different kind of information that were available. And most of them were around photographers by the National Center of Research, Scientific Research in France, CNRS. And one of the big work for them was to collect all these kind of information to store it in a specific database. So they've been working to have a specific application that they developed. It's a national solution called IOLI. And this was a huge and a big part of the process was to collect in order to understand how it was built, with which materials, how it had evolved in the past, et cetera. And this was very important for the success of the future reconstruction. Jan Hoffmann has a question. Which software do you recommend for modeling BIM existing buildings? What software do you recommend? Maybe the question first to Ulrich Hartmann. To me, you mean which software I have a recommendation for sure. And that's a common data environment to share all this information correctly in a sufficient and efficient way. I mean, it's taking off all those information you mentioned, Emmanuel, by laser scanning and so on, creating then BIM models from that. But you have to share some information between all those disciplines. In your case, you say BIM 360, your tool is the most advanced. And of course, there are others like our Aconics CD could do that. Emmanuel, the question is up to you. So the question was about... Which software do you recommend for the existing buildings? It's a good question. Actually, it can be a mix of different software because we realize that in some specific cases, let's take the example of a statue, which is on a cathedral. We see that by experience and we work with, for example, a French company which is a long experience company because they've been working that field for more than 25 years. And they use a collection of different software. So they use Revit mainly and they use also 3ds Max. They use sometimes Rhino so for some specific complex shapes that you cannot model with a traditional BIM software. It's interesting also to see that CAD is still very important because 2D documentation is a very big part of the process. So it would be a combination of using AutoCAD as a tool. And we were mentioning point clouds. So for point clouds, you would use either the software coming directly from Leica, laser scanning system, or Faro, or Docker, or whatever, or Trimble once. But then after, in order to treat and analyze information, you could definitely use software like Autodesk, RECAP, et cetera. So there is not one single answer. It's always a mix and a smart way of using different kinds of tools. And as Ulrich mentioned as well, there are different kinds of CDs when you want to share the information and transform it into a digital twin. You can also make different choices. Leica, do you also have recommendation because then each of you has the chance to give a recommendation for the construction software using for existing buildings? I don't think that in that context we should promote any particular vendor or software. I agree that we should look at the requirements and then pick the appropriate tool that gives us the best results. Okay, that's for sure. I can only say we're using algorithms. We are not using a particular software. We're using AI and we're using algorithms to produce exactly whatever provides the best output for whatever reason. Okay. Maybe one remark from my side, Denise, if I may. And that is that I mentioned models are made for purpose. And if you take off an existing building, for what reason do you do that? For reconstruction or for reusing material or what is the reason? And the reason determines the right tool. And not start with a tool and then do what you can do with the tool. It's for checking the requirements by what is the intended need for this information you take off? Well, let's go back to the beginning when I mentioned the huge potential for climate, environment, the potentials. Yeah, what social significance do you as experts attach to this topic? Yeah, just give examples. I can say something to that as I may. So Uli said, music panel of the UK approach. And I think they put a very good vision out for that. And it's very simple. It says building assets better, building better assets. Think about that for a second. So just do what you do, do it in a better way using better tools, being more collaborative, et cetera. That's about the design process. But the other one is about building better assets. That's not better in the sense of the right assets in the right place. So how do we know what we need? And I come back to my question. We as the society and as members of society we consume services like we get on trains and buses. We get treated in hospitals. We go to universities, et cetera. And all these services are provided on the back of the built environment. So where do we need the next railway to go? How many hospitals do we need? Where do we need the hospital to be? How big do we need it? So that's all the question, which eventually then the construction sector will design and build the thing. But we as the society, we determine where it's needed. And that's where I think we should look at where feedback loops from how people consume assets is really important. And that's where we should stop looking at the micro-micro level of just saving a few quits in the design process but also start looking at the bigger picture. So what's the embedded carbon really? And how is this building, which was designed for a certain purpose and for a certain energy consumption, how is that delivering to the expectation? Is it actually really only consuming that or is it consuming a lot more? So where is then the fault, whether in the design or whether in construction and the materials or just am I from the start? Anything else to add for examples, for the potentials? The potential is huge in any phase of the project. So we've been talking about the design phase and mainly in the construction and operation phase and it's obvious that without digital approaches and it's difficult to reach the targets that have been defined by the European Union, for example. You know, there is also this big renovation wave at European level and if we want to massify, so and if you want to reach these goals of having better buildings, being able to manage the energy that they will be consuming, making them better in terms of efficiency, et cetera. If you want to massify because we realize that in each country we have a big database of existing buildings that we will have to renovate. We can't imagine that we will destroy them all, et cetera. And if we want to massify and to reach as soon as possible these targets, we definitely need to base the R strategy on digital technologies, on drones or whatever. I mean, BIM is a kind of, it's an epi-phenomen. It's only one part of the solution. You have so many, I mean, Ileka was speaking about AI, about generative design and all these kinds of things. We have to grab all what is available in terms of innovation in order to reach all these goals. We cannot imagine, when I hear sometimes and Ulrich was mentioning, the BIM adoption in Germany, we are the same issue in France. How can we imagine, how can public authorities imagine that they will reach the targets that have been defined at national level or international level, without basing their strategy on digital technologies and BIM, it's impossible. So it's very important at Autodesk, we think that is very important because we apply this to ourselves, first of all. So we would like to see all the public owners, et cetera, all the governments to take this seriously into account and to use all what is possible in terms of resources to make this happen faster. Ulrich, you just saw the question, a question especially to you. What are the limits of the data processing for large buildings, such as roads, railways or power lines? Yeah, I mean, that's a typical question in terms of megabytes or gigabytes. There is virtually no limit, but in terms of how could we understand these data and data mining in those cases, it's, I just can come back to the phrase, models are made for a purpose and this is not, that should be the driving force. Limit the information inside the model to the absolute minimum and then you never reach these limits in terms of gigabytes. It's more about having the right decisions on the right data. So technically, I would say there's no limit. Eka? I have a question to Immanuel actually, because what we observe here in Germany now is that a lot of clients, especially in the public sector, they want us to produce a BIM model from an existing asset in a proprietary software so that it can then be handed over to an architect or an engineering firm for the next phase of a refurbishment or conversion or rebuilding or something like that. Is that also something that you see happening in France? Because I see the limit here that if we did that, if we would produce a full copy of an existing asset, there's still, as earlier said earlier about the rental, there's still a whole lot we don't know about this building. We can't see, we can't see in front. We can't always see what is behind the clouding or something like that. We can still produce a geometry of what we can see and we can make some assumptions but there's limits to that. So in Germany now, the process, what the clients would like to see is that they then give this model to an architect and the architect takes it, puts it into his design software and starts editing on that basis. And I don't think that this is going to happen because they would adopt a lot of liability and risk if they did that. So they would, I see that they would always only use it as a reference, as a background reference and then start their own new model and new design. But I would be very keen to hear how that is in France. Do you see a similar tendency to do that and do you see similar limitations or is this just Germany being over-anxious? No, I think so, yes, Ilka. So it's kind of similar in France. Maybe the difference is that we have companies specialized only in scan-to-beam producing models specifically for owners. So generally, so most of the time, these models would be produced to nurture an operation and maintenance system. They would not ask the architects because first of all, this is not, so architects don't like these kinds of, I would say missions. I agree with you that there are lots, there are many limitations in this kind of approach. Generally, the owners are requiring IFC model. We see lots of limitations also due to the fact that, as you said, there are so many things that we are not able to see on the lease or the systems, et cetera, which means that we have to have a specific strategy. Sometimes we must break specific elements in the buildings, et cetera. So there has to be a strategy around that. But generally, we have some specific companies which are specialized in that. And most of the time, they partner with companies like software developers specialized in operation and maintenance in order to define the right level of detail, whether it's geometrical or the information that you want to have access to if you want the operation and maintenance system to be efficient enough to give some good data back to the owner afterwards. But it's a real issue. I have an idea because earlier you mentioned how exciting it is to create standards. So what we might need for existing assets, we might not need a level of maturity standard. We might need a level of reliability. So there are some things that I know for sure, 100% fact. And there are things where I've made it an assumption on the basis of something and then I can pass that information on to someone else. Would you ever think it would make me a standard to do? Yeah, it would be. I fully agree with you. But you know, one of the big concerns is that in the case that you were mentioning, we are lucky because maybe the owner is asking for a B model or he's asking the architect to produce a B model. There are also lots of cases where there is only paper drawing. And then it's even more challenging. And this is where we see also startup companies creating some specific algorithms which allow to recreate, I would say a basic B model, you know, based using Blueprints and recreating IFCB models then after are reused for operation and maintenance purposes. So we just saw that there are a lot of questions and right now we try to share the chat window with all of you because there are special questions to the three of you, to Ilka, to Ulrich Hartmann but also to all of them. So please give me the whole chat that we can read that together. Maybe we start at the bottom. Ilka, are there already examples of databases that hold BIM data as part of them for lots of buildings in cities of the UK? If so, we would have a good database for comparing Notre Dame with Cologne Cathedral, for example, or one office building with another in the same city. Who could hold those databases? Ilka, my? Yeah, yeah. That links to the question above from Pauline about the algorithms behind that in what role does AI play? I can only speak for ourselves. So we have created over time an enormous database of objects from the real world and that's the difference. So our database contains all sorts of windows and everything that we've extracted from videos or photographs from the real world and they look like real world objects. So therefore they're different from design tools which are generic representations of something that doesn't exist or has been extracted from that. So in the AI, the algorithms and the artificial intelligence is trained to detect and identify objects in a video or in a point cloud or a photography and replace it with the object from our library and that's how we produce object-based models from existing stuff. I hope that answers this question. Who can hold those databases? Well that way comes to politics. This is a huge market for innovation and for competition and for driving better outcomes through a very good strategy where politics and politicians can create and incentivize a very competitive and innovative market by getting this right. So why not a lot like hold the database like that there might be hundreds of other companies holding database and that's a healthy competition and that's something where I think we don't need one central database that's the old baby one. That's something where we need competition. Thank you. There's another question. Is it possible to scan infrastructural services such as underground, electromechanical pipes, cables, et cetera? Yes, it is possible. It already happened. There were lots of proof of concept in the US. I remember an example for example in Las Vegas and we see also I'm sure in the UK that it's already the case because there are already some startup companies in the UK making small robots that are able to go in the different kind of system networks in other streets, et cetera. And in France we see also many examples of companies being able to produce these kinds of infrastructure information. Okay, do you agree? You're right, I think the mind of the way of examining the underground without penetrating it perfectly. Yeah. Perfect. I think all in all we had the huge topics. There was another for the cathedral. I guess we didn't answer yet how did you benefit from the BIM model in the facility management for operation but the facility management will start in a few years or? Yes, it's a good point. I saw the question. So actually we are not in this phase yet. We are discussing with the Diocese which is the organization, which is the owner actually and they are interested in this topic. It has not been defined yet although they see lots of benefits and added value that they could get from having a BIM model for the operation and not one phase but this has not been defined yet obviously because for the moment I mean the very strategic part is the reconstruction of Notre Dame. Okay, I have another question. We heard a lot about the potential and maybe it's also time to come to an end but there's one question I have to all of you when we're talking about the potential and again in your words, where are we right now and what could be in a few years or in a short period of time? Well, if I may start, it's hard to say but we are still at the beginning I would say and it's a permanent journey. So as you can see the digital twin story is a very exciting one. And if you look at the things done in the UK already they are on the journey already with their center of digital Britain they are already putting in real data from existing urban take offs into a huge database in the National Archives. So that's what the things will go I think to include and integrate everything. Dika, what do you think about that questions? Where are we today with them and what about the potentials? There's still a lot of misunderstandings around them and we still seem to create costs rather than generating value from the whole process. So I hope that we will very soon be through that phase where we then start to really realize that we can make things more efficient and simpler, slicker. At the moment every BIM project that I see seems to drive people out for the same math because they think, oh my God, this is all so complicated and why can't we do it as we did it before? And it should be the other way around, it should be like, oh, I never want to go back to how we did it before because this is so much better. And there's only one project that I've worked on and that was in the UK where this was the case where people after a few weeks said, oh, absolutely brilliant. But that requires a lot of very educated clients, a lot of processes, so not just looking up how do we model things on the software that we use, but really it's the whole collaboration process that only mentioned earlier. And if we then start to collaborate and work together, all is hearing to the same structures and processes, et cetera, then it becomes so simple and really, really valuable. Thank you. Ulrich Hartmann, last round up to you. If I may add maybe to what Ulrich just said, I think that the big challenge is that the AEC industry, especially in Europe, is very fragmented. We have lots of SMBs and VSBs, very small business companies and small and medium business. If you would draw a curve about the adoption of BIM, you would see that you have the major companies, the big companies, which are on the top of the curve. They have no problems because they have resources, they have a strategy, they have very talented people, et cetera, but if you look at the VSBs and the SMBs, they are really at the bottom of the curve and the problem is that this curve is kind of amplifying over the years and we should definitely not leave anyone on the side of the road because there is a risk of big disruption for all these small companies and medium companies and if we want BIM and digital approaches to be successful, we have to have everyone together, working together, collaborating together. If not, it will not be succeeding and we see also in the UK that although they are leading the way in Europe, they ask to themselves this critical question of how should we do to bring all the AEC ecosystem together on the road of success and this partially depends on the desire of governments, on the resources that they put, on the money that they put on the table and we have to work together in that and not forget anyone and in my opinion, this is what is more important actually. Thank you very much. I just had a look on my watch and we are talking right now for 80 minutes. Time is flying but I would suggest that we will meet in September at Intergeo Hybrid. You can participate digital or in Henova at the Expo, Henova Expo and there will also BIM a huge topic in the conference and of course in the Expo with all the companies and their solutions and I guess because there are so many more questions we hadn't time to talk about how integrate BIM when talking about citizen participation and so on, there are some more few topics that just had not space in that short hour of the Intergeo talk format. So I would like to say an official thank you very much for joining us and say goodbye until September or until our next Intergeo TV talk which will then be at the 18th of June about Smart City and thank you very much and if you like you can also stay right now also in the chat, ask some more questions if this is helpful but thank you very much Ilka Mai from LockLab Consulting Emmanuel Di Giacomo from Autodesk and Ulrich Hartmann from Oracle it was a pleasure and I hope to see you soon.


Let's have a look at another example. In this reaction two bromine atoms are combining to form a diatomic bromine molecule. An experiment has been performed where the initial concentration of bromine atoms is varied systematically and the rate of reaction is measured. As you can see for this reaction when the bromine atom concentration doubles the rate quadruples. You can see we go from 0.1 to 0.2 and the rate goes from 1.2 to 4.8 moles per litre per second. If you look at the first and third experiments you can see that when the concentration triples the rate is multiplied by 9 and from the first and fourth experiments you can see that when the concentration quadruples the rate is multiplied by 16. If you line all this up you can clearly see that the rate is not proportional simply to the concentration of bromine atoms but instead to the square of their concentration. And if we want to convert that to a proper equation we need the rate constant as before so it becomes rate equals K Br squared.


Hi everyone! My name is Sheema, I'm a librarian here at the San Francisco Public Library. I want to share a song with you today called The Green Grass Grew All Around and this song has a lot of different variations. You can add a lot of different verses. It's fun to just think of ways that you can think of the things that would be on a tree and that you can act out. You just keep adding on and it's fun to go slower and faster with it. But I'll show you my version and you can think along and you can make up your own version at home. Okay? So here we go. It's on the tree, the tree was in the hole, the hole was in the ground, the green grass grew all around and the grass grew all around. There was a twig, it was on the branch, the prettiest little twig, not you ever did see. And the twig was on the branch, the branch was on the tree and the tree was in the hole, the hole was in the ground, the green grass grew all around, all around and the green grass grew all around. There was a nest, it was on the twig, the prettiest little nest, not you ever did see. The nest was on the twig and the twig was on the branch and the branch was on the tree and the tree was in the hole and the hole was in the ground, the green grass grew all around, all around and the green grass grew all around. There was a bird, there was in the nest, the prettiest little bird that you ever did see. And the bird was in the nest, and the nest was on the twig, and the twig was on the branch, and the branch was on the tree, and the tree was in the hole, and the hole was in the ground, and the green grass grew all around, all around, and the green grass grew all around. There was a beak, there was on the bird, the prettiest little beak that you ever did see. Let's see, and the, equals on the bird and the bird was on the nest and the nest was on the twig and the twig was on the branch and the branch was on the tree and the tree was in the hole and the hole was in the ground and the green grass grew all around, all around and the green grass grew all around. So you see that it helps to think of things that you can say quickly and you can act out quickly otherwise it's pretty hard to do this song without losing your breath. That's the green grass grew and thanks for visiting the San Francisco Public Library Storytime Tube box.


President Mohammed Buhari has launched a new long-term national development plan, the Nigerian Agenda 2050, which is aimed to ensure that the country attains a per-capital GDP of $33,328 per annum, placing her among the top-middle income economies in the world by 2050. The president today inaugurated Niger Agenda 2050 before the commencement of the meeting of the Federal Executive Council meeting at the Council Chambers of the State House in Abuja. According to him, the plan has the vision of dynamic industrialized and knowledge-based economy that generates inclusive and sustainable development for the country. 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.


It's too hot to be stuck in traffic Hi, I'm Lavi and I'm Oli and this is our hero bumblebee together We are attempting a Guinness World Record to become the youngest pair to circumnavigate the globe by motorcycle Join us for season three here in South America Wow looks like a wedding cake Amazing There's our lovely host It looks amazing Good morning world. Welcome back to the channel. It's day number 193 on our circumnavigation around the globe by motorcycle We're here in Paraty where we've been for the last couple of days. It's been actually very rainy and very gray, but Look at it now The sunshine is back this morning. It is blue skies And it's the perfect day to get back on the road. So let me show you guys where we're heading today So we are here in Paraty and today we are going to be continuing our way down the coast Taking a small ferry over to the island of Ila Bella So really really exciting because we were contacted by a guy His name is Daniel and he has actually a property on Ila Bella And he said guys if you want and you're around you can just stay at my place So we get to spend the night on Ila Bella the beautiful island That's literally what Ila Bella means. It's about four hours from here And we can't wait to get down there and check it out. So better hit the road. Let's go 456 Obrigado First thing Juice for Bumblebee. Oh, yeah, because we've already done a hundred and seventy seven miles on this tank Look another friend of Bumblebee here. Haha. Yeah Little Suzuki yellow scooter iconic yellow. Wow. It's so clear skies today You wouldn't believe that for the past two days It's been wet constantly gray skies Raining and then just on the day that we are due to head out down the coast The skies open up and it's amazing again. How lucky It's like lucky and unlucky because the Sun is also incredibly hot But it's beautiful to ride in so 50 50. We just need to get some speed Exactly. So it's about 85 miles Down to Sal Sebastião, which is the small town Where you take the ferry across to Ila Bella the place that we're due to stay for tonight is called Casa Mar and it's owned by Chris and Daniel and we don't know Chris and Daniel, but we just got a message on Facebook from Daniel Yes, I think they must have seen one of our hundred posts Haha But it's super nice of them to invite us for a night to stay. Oh, yes, since we talked to them I'm just dreaming about it. You know, I'm like, let's go. Let's go. Let's go Yeah, the place looks super super nice And if the weather stays like this then we've just got to get down there Yeah, we just got to get down there Yeah, because it's really special for us to be invited in a really nice place We're staying in nice places, of course, and we love to stay in our tent But to have an experience like this is just amazing and to meet people who are interested in the journey in general It's just great. So can't wait to meet the guys Hola. Just full of gasolina normal. Obrigado Obrigado All right, just up and ready to go. Wow, this is an amazing Forested green area to start our day's ride. Look at this. I just saw a sign for some Stagge deers Watch out for the big deers. But this area is actually a protected area. What's the name of this area? area de protectao ambiental de Carlos Yeah, exactly exactly like this exactly like that Yeah, I can see here on Google Maps. It's a huge area With some islands as well around forested hills around. That's what we like to see. Yes So we have just left the state of Rio de Janeiro And I've entered our second state here in Brazil Sao Paulo Look at the ocean in front Oh, yeah protection of nature is epic I love it. Just to see such an old forest around is we're really really comfortable and nice feeling I just want to see a sloth Where are you slothies? I know you're in there. Run from me. I will find you. I could see the coast just a second ago For me it's quite nice Because I can look right and left and I can really see everything and you have to concentrate on the driving I have to concentrate on the what? I'm just looking for a sloth. I don't know what you're talking about. Sweetheart A little bit of road works more like Landslide works. Look at this.  Wow Look at this crazy view Wow Jurassic Park Here we go. I just saw on the sign the park is called Serra do mar Which means I think mountains of the ocean or ocean mountains Yeah, and if you see them then you'd know why they're called like that Exactly Park estadual Serra do mar So we're about two hours into the ride now is getting busier and busier We've been pretty much stuck in a queue of traffic and there's been more towns popping up along this coast But nice beaches Wow, yes But with those nice beaches comes more tourism comes more tourists more traffic Yes, it's taken us two hours to cover about 60 miles. So I think that it's time That we take a little break and chill out for a minute Yeah, exactly Let's eat some of our stolen breakfast Beautiful Just like all the stuff from our breakfast when the host wasn't looking Lavi just Stuffed everything into our tupperware was like go go go go go So now we've got loads of cake and cheese balls You're a real survivor a real bunny Running alongside the ocean Yeah, wow Brazil is one long beach The coastline is pretty much one really long beach.  Yeah, this one there. Yeah Yeah, it's I think that's an island. Yes Do you think that's Ila Bella? Maybe? Maybe there is Ila Bella Just 23 miles left to the ferry port in So, Sebastian We're just Coming through a town called uba-tuba, which is quite funny her name, but the traffic is not funny It's too hard to be stuck in traffic, I think it's like 30 degrees and the bike is just releasing heat as well, it's like Sitting on a radiator Yes, it's like sitting on a radiator inside a sauna. I'm dreaming of Casa Mar Yes, we too. There it is in front Just on the other side of this narrow channel, look at that. It looks huge. Hold on a minute It's probably not my way. Hey Oh, it is. He's going that way. He's going that way, no Confused. Our port was straight. Oh, okay. Okay. Okay, okay. Okay. Porto Let's go. I think we'll just follow everyone else. Hey, okay. Yeah, what do you think? Yeah, I think so Accesso balsa. I Think it's just straight Hold on a minute Traversa Ila Bella. Okay, I could probably go through here. Okay. Yeah, okay. Let's just go Cool, according to my map, it's like it's like just straight ahead and that's the ferry This guy just showed us the way to go to get to the moto entrance Which is not where all the cars are over there. We've actually got our own little entrance So we get to skip the queue. Yeah, that was a little bit complicated for us To know which way to go. Yeah. Oh Hello, yeah, I Think he said just cash cash only So it's cash only here actually to get on the ferry and we have like no cash But luckily I've got a ten reales note in a money collection in the back box Guys come from England and and Germany Germany. Yeah Yes, yes Okay, cool, so just in the middle. Okay, awesome. Thank you Thank you. See you. Yeah. Oh, that's nice Oh my god, this is a little bit tight it is There's a line, okay a line of bikes. I guess that's the good thing with the motorcycle We get to skip the queue quite often. That's useful. Oh Yeah, well, it's not really a ferry as much as like a platform.  Wow. Oh my god, look at this bridge. Oh my god No, oh my god, that's a little bit of a dodgy one that was Oh on the platform Yeah, he said I can go just straight to the front. Okay, just to here. Oh, yes Fantastic. All right. It's time to get our gear off We only just got our stuff on in time Really just in time. Oh my god. What is that kerb? Whoa? Whoa? Crazy Yep, okay.  Oh my god All right We have arrived. Yes Hello, that's it. That's it. We have made it To land to Ilebella. That's awesome. Kassamar. We are coming. Yes 26 minutes And we are there 26 minutes Ten miles Ten miles. Yeah How big is this island? Shoot. Whoa. Absolutely shoot. I thought we were just gonna come off the ferry and it would be there Ten miles Well, I guess our journey is not over for today then Ten miles to go We're down to the quiet side of the island now We have passed all traffic jams and queues and this is nice and quiet down here and we have just a couple more miles to go to reach Kassamar We've entered the state park for the island Ilebella Park Stadiual and actually most of Ilebella is This national park or this state park protected area So it's pretty much only populated along this side the side that faces the mainland and If you see on the map the rest of it is totally unpopulated uninhabited Wild Totally wild Whoa Is this one here? Ah Yes, it is Kassamar Whoa, look at this. Wow That's cool. That is cool. It's like a gate into a jungle Okay 456 All right. Yeah, in we go and we go Second I'm just gonna get over the bump here Wait a minute.  Okay Ah Yeah, oh sweetheart perfect. Oh my god. Whoa, we made it Wow, look at this place Ocean views Beautiful, that's crazy Out here is just pure coastal rainforest look at that Oh No, oh you're guilty. Oh you're kidding. We have arrived In paradise Truly arrived in paradise this place here is Unbelievable the nicest place I think we have ever stayed in ever Pretty much ever. I would definitely agree with that and this room is just perched on the edge on the ocean front. It's absolutely perfect The interior design of our room is just so like it has so much taste like the art and the colors and The materials are so incredible. Yeah, Daniel told us that his wife is an architect and He's the builder and together they have this unstoppable force to make something Like this Yes, so talented this guy's. Oh my god So luckily it's quite early in the afternoon that we can enjoy this place here for the rest of the day Tomorrow we have to move on already unfortunately, I would like to stay here just forever We did about 100 miles today, which is about 160 kilometers plus a nice little ferry ride as well tomorrow We will make our way to board Sao Paulo, which will be really interesting to see a very very big city Like the most populated city here in Brazil. It's gonna be different to where we are now. That's for sure So that's it from us today. We hope you enjoyed the episode if so, please give us a thumbs up Subscribe to the channel share the video with your friends and family comments below. We will see you next time straight cruising Head is watching out for number one.


Hi and welcome to the session. Today we will learn about minors and cofactors. First of all we will start with minors of an element aij of a determinant is the determinant obtained by deleting its ith row jth column in which the element aij lies and minor of an element aij is denoted by, for example, if in the given determinant we want to find out the minor of the element a32 then for that we will delete the third row and the second column in which the element lies and thus m32 that is the minor of the element a32 will be the determinant obtained by deleting the third row in the second column so it will be a11, a13, a21, a23. Now if the determinant is of order three then the minor of any element will be of order two that is one less than the order of the determinant that is one less than three. Now let's see what are cofactors. Cofactor of an element aij denoted by aij is defined as aij is equal to minus one to the power i plus j into mij where mij is the minor of the element aij so here the cofactor of the element a32 denoted as a32 will be given by minus one to the power three plus two into m32. Now we know how to find out the minors and cofactors of the elements of the given determinant so the value of this determinant will be if we expand it along r1 then it will be a11 into cofactor of the element a11 denoted by a11 plus a12 into the cofactor of the given element that is a12 plus element a13 into the cofactor of this element that is a13 which is equal to sum of the product of elements of r1 with their corresponding cofactors. Remember one thing that the sum of the product of elements of any row or column with the cofactors of any other row or column is zero. Now let's move on to our next topic that is a joint and inverse of a matrix. So first of all let's see what is a joint of a matrix the joint of a square matrix a given by aij of order n is defined as the transpose of the matrix given by aij of order n by n where aij is the cofactor of the element aij the joint of a matrix is denoted by a joint of a for example for the given matrix a a joint of a will be given by transpose of the matrix of the cofactors of the given elements which will be this one and its transpose will be this matrix. Now suppose we are given a two by two matrix a and we want to find a joint of a then there is a shortcut method for this what we will do is we will interchange these two elements so we will get a two two over here and a one one over here and for these two elements we will change the signs that is from plus to minus and from minus to plus so here we already have plus so this will be minus of a one two and minus of a two one so this will be the a joint of matrix a now let's see some important results first result is a b any given square matrix of order n then a into a joint of a is equal to a joint of a into a which is equal to determinant of a into i where i is the identity matrix of order n now before moving on to our next result we need to know some important properties that is i square matrix a is said to be singular if determinant of a is equal to zero also a square matrix a is said to be non-singular if determinant of a is not equal to zero now we'll move on to our next result that is result second this is states that if a non-singular matrices of the same order then a into b and b into a are also non-singular matrices of the same order now let's see the result the determinant of the product of matrices is equal to product of their respective determinants that is determinant of matrix a into b is equal to determinant of matrix a into determinant of matrix b where a and b are square matrices of the same order the fourth and the last result is a square matrix a is invertible and only if a is non-singular now let's take one example here we are given a matrix a and we need to find a inverse if it exists so let's find out determinant of a this will be equal to 14 which is not equal to zero this means matrix a is non-singular now by the result four we know that a square matrix a is invertible if and only if a is non-singular matrix so this means matrix a is invertible or a inverse exists also we have a inverse equal to 1 upon determinant of a into a joint of a so this will be equal to 1 upon 14 into a joint of a that is 3 minus 4 2 2 in the same way we can find out the inverse of a square matrix of order 3 with this we finished this session hope you must have enjoyed it goodbye take care and have a nice day


Hey guys and welcome back to the channel. This quick video is an update for a new YouTube series that I'm starting this week.  So for folks who are already following us on Instagram and Facebook, you guys know that back in September, end of September of 2020, I became a US citizen. Yay. And to be honest, that was such a happy, joyful moment for me. And before anything, I do want to say thank you because you guys' comments and messages, they were so lovely and so kind. So thank you so much for sharing that beautiful moment with me. So became a citizen at the end of September 2020 and not too long after I obtained my US passport. So to be honest, I was a little bit hesitant before starting this series in which I want to share with you the whole process for everyone who's going through the naturalization process. And by the way, that's the process through which if you were not born in the US and you're not a citizen by birth, you do have to go through the naturalization process to become a citizen. So there were at least four people over on Instagram who reached out to me who are going through the naturalization process and they wanted to know something specific. They have some questions that I already answered, but I thought these series are going to be probably very helpful for people who are going through this process at this point of time because things are a little bit different during the pandemic right now. But like I said, I was a little bit hesitant because that's not related to hiking and backpacking, but at the end it is related to traveling. And I know with an American passport right now, I would be able to take you guys with me to new places around the world, new tracks, new trails that were otherwise difficult or impossible to go to. So bear with me as we go through these series. But for those of you who are interested in this topic, I will dedicate these series to talk about how to apply for your citizenship online, step by step, all the detailed tricks and tips to make it successfully. I will share with you my history for my case just to show you how long it took for me from step A to step Z, how to prepare for your biometrics interview, the civics test, the oath ceremony, how things are different right now with the pandemic. I will also be talking about what should happen once you obtain your citizenship. I'm going to share with you how you can apply for a US passport. That was the most exciting part for me. So I'll show you how you can obtain it as fast as possible. So these are the topics or the ideas that I have right now in mind for this series. And by the way, these series are going to be coming out on a daily basis. So if you're not already a subscriber, make sure you subscribe and make sure that you ring the bell so that you receive notifications whenever a new episode is out. With that, I hope that you guys will find these series to be useful. And if you do have any specific questions or anything specific that you would like to know, this is the right time and the right place where you can leave me a comment and let me know what you need to know. I do also know that there are a lot of French and Arabic speakers on my channel. So no matter what language you speak, I know that this process is both exciting but also time consuming. So please do reach out to me if you're not comfortable sharing with the public here on YouTube, just send me a message and I will respond immediately. With that, I'm pretty excited for you. If you are going through the naturalization process, let me know. I would like to just congratulate you and celebrate you. So yeah, that's all I had to share with you guys today. Yeah. And with that, I hope that you guys are having a great weekend and we'll talk to you very soon. Bye.


Russians still face stiff resistance in Bakhmut. Russian assault teams captured four urban areas in Bakhmut and paratroopers provided support and immobilized enemy forces on the city's outskirts during the special military operation in Ukraine. Russian Defence Ministry spokesman Lieutenant General Igor Konoshenkov reported in the Donetsk direction the assault teams captured four areas in the North West. Western and Southwestern parts of the city of Bakhmut. Airborne force units are immobilizing the enemy on the city's northern and southern outskirts and rendering support to the assault teams' operations. The spokesman said, Russian troops tried to sever important supply routes into the eastern Ukrainian city of Bakhmut and thereby put more pressure on defending forces Ukrainian officers said. Ukrainian military analyst Oleksandr Musyenko said districts were rapidly changing hands in fierce fighting. Ukraine is successfully conducting local counterattacks, making it difficult for the Russians to capture Bakhmut. Musyenko told Ukrainian NV Radio, at least 4,000 civilians have been killed in the fighting in Bakhmut according to estimates from Kyiv and thousands more soldiers from both sides. According to the Institute for the Study of War, Russian military leadership is increasingly prioritizing completing the city's capture before the start of the Ukrainian counter-offensive. But Kyiv has almost completed its preparation for a counter-offensive against Russian forces. According to Defence Minister Olexiy Reznikov, his country's troops are ready to go ahead, adding, As soon as there is God's will, the weather and a decision by commanders, we will do it, he added. Globally speaking, we are to a high percentage ready.