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Bc an adjaccncy matrix ol # graph G-Thcn thc maximum dcgrcc in Gea=Nonc o/ thc other [email protected] 40 2C 5...

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Bc an adjaccncy matrix ol # graph G-Thcn thc maximum dcgrcc in Gea=Nonc o/ thc other [email protected] 40 2C 5

bc an adjaccncy matrix ol # graph G-Thcn thc maximum dcgrcc in Gea= Nonc o/ thc other choices @ 4 0 2 C 5



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In Exercises 41-46, use the matrix capabilities of a graphing utility to find $AB$ if possible.

$A=\left[\begin{array}{r} -2 & 4 & 8 \\ 21 & 5 & 6 \\ 13 & 2 & 6 \end{array}\right]$, $B=\left[\begin{array}{r} 2 & 0 \\ -7 & 15 \\ 32 & 14 \\ 0.5 & 1.6 \end{array}\right]$

Okay, so you have this point it would be. And now the front, the shortest distance between this point, it's simply a streak going. So let's go ahead and catch. This points on. It's French. Okay? He's four negative. Far somewhere here, Right? Onda Bi is 12 3 That should be somewhere up there. Now let's join these two. So we need to find Point C and we've been told that see, Israel, this line crosses the X axis, right? So meaning seem must be at that point where this line crosses over eggs axis. So this is redefined it to find the export. And Lucy would be find the middle off this distance between A and B. So here we have an X coordinate travel guide. And then here he had a excluding it'll form. So really deferred the exact middle at this distance. So that would be for most 12 giving the 16 divine light too, which is eight. So we actually ate on the wire recording it. It's obviously do because it's on the X axis, right? The answer of the textbooks, his 92. But that is false.

Okay, This is actually to do this question would be too far in this equation of a lie. Or if you have crossed me, but you can just catch and slime and b dizzy 12 3 speed. Right. So first recon find out the slope and that gives us a slope of one. Next we confront the white cept, which is we in this case, it's negative line. So that should give us a line looking something like that. Right? Damn you. So we need to find C. We've been told that scene lies on the exactness, right? So, in essence, we're fighting the point with this line Crosses, eggs, axis. How do you find that? At this point, we know why. Physicals to zoo so we can put zero here for this, right? And then so for X that gives us excess nine. So the coordinates of sea would be nine there. All right,

Now we're here. The mattresses that has been given to us is the metrics. A having the elements minus three eight minus 68 again. Then minus 12, 15, 96 five minus 11 and five. I'm just copying the metric that is already given to us in the question itself. The other metrics, you know, by B is having the elements. 316 24 15, 14, 16, 10, 21 eight. Minus four pain. Okay, so these are the two mattresses. We just have to find out the metrics. A b. Okay, So for that, let us first find out whether it is possible or not. So let's remind the order both the mattresses. The first Matrix A is having three rules on four columns. That means it is a she before ordered metrics. Whereas the city metrics B is having four rows and three columns. Right, So it will be up three by three Ordered metrics on the square metrics off order three. Right. So the product is possible. Why? Because I can see that the number of columns off the first metrics is the same as the number of rows of the second metrics or I can see the middle to industries asking So we can easily, due to my deep product, Patrick's baby. Now the question arises. How do we find out the product mattress? So for that, we simply take up the door product off. The first wrote the first metrics and the column of the I mean the first one off the second metrics. What I mean by door product is simply minus three. Thanks three plus eight times 24 minus 16, 16 plus eight times age like this. Okay, so as you can see, I'm just taking on the door product off the off the first nine tricks and column of the second one. Now, if I talk about the second, uh, element, I mean the element of the first round. Second column. Now what I'll do. I just think of the door product of the first row off the first Matrix. But the second column, the second metrics now. So that will be minus three times one less eight times 15 minus six times pain Last 18 minus four like this. Alright. Similarly, for the next one, what we'll do is again minus three times six. Now, just take up the roof. I mean, the first from the first mattress and the third column under sticking mattress. So that will be minus three times six plus a thanks would be minus exchange 21 plus a thanks. Thin like this. Okay, so it will be something like this. So in the same manner for the second one, what do you do? Is you just take up the I mean, for the second room. I'm going to take this second rule the first mattress and the three columns. All the other metrics. So that B minus 12 times three last 15 times 24. Then last nine times 16, then plus 16, 8 like this. So the same manner you can get your mind, the other elements as well. So I'm just quickly multiplying it here itself. Is he? So what? I'm going to get this. 151 25 48. 516. 279. 387. 47. Minus 20 Hand. It is a right. So we all know how we did this on as they say in the beginning. Also, it will be a three by three other matters so you can see in the product metrics. I'm getting three Rosa, three columns, so this is really very simple, right? Uh, just a quick look up again for a project Patrick's. What we do is we just take complete don't product off the rules of the first Patrick's and they call them off the

Now we're here. We've been given to mattresses. The metrics is given to us as 75 minus four minus 251 Pain minus four. Minus 70. I'm just noting down the elements early on mattress be is given to us as it is a tributary order metrics. Or I can say it is a square matrix. Okay, 81 or minus 42 and minus it. Like it. Okay, we're supposed to find out the matrix A B. So for that, let us check whether we can multiply these two mattresses or not. So for that, what we need to first check this. Let's check the order for us. So oh, metrics is off the order three by three. Where, as they say in one, is also of the order. Three bucks, three. So that means the Middle East to indexes are saying you think that the number of columns of the first mattress is equal to the number of rows of the second metrics. So, yeah, we can multiply the two mattresses. Now the question arises. How do we multiply the two mattresses? So for that, we just take up the dot product of the rules of the first Matrix and the columns off the second Patrick's. So what do I mean by this? Is seven times two plus five times aid plus minus four times minus. For like, if I talk over the next element, then what will do will take up the door product off the rule of the first metrics. But the second column off the second Patrick, some minus to plus five times one plus minus four fines to like this on if we talk about the food called Word column, I mean the element that belongs to the first round. The third column, then the stick of the door product off the first room on the third column on the second metric. So seven times three. That's five times four plus minus. Four times minus eight. Like this. Okay, again, over here. What? I get ISS simply, um, minus two kinds. Too less five times eight. Yes. One thing minus four. Yes. So this is really very simple way. Just have to multiply the two mattresses as I'm doing over you. Now take the second row and the third column minus two class five times. War plus one times minus speak like this over a year. Now take the door product off the third row of the first metrics and the first column on the second metrics. Minus four times eight minus seven times minus four. Then 10 times minus two minus four times one minus seven times, two for the last one. Just take up the door product off the first of the story off the third off the first metrics and the third column the second metrics minus or times so I can see, then minus seven times minus eight like this. Now, the last day, we just need toe Simplify this so on, simplifying that what you will get is 70 minus 17, 73 30 to 11, 6, 16, minus 38 70. So this is the matrix, a B that we were supposed to find out work here. What


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