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Om2m Scale4m97 -A+B-AA1-2B9A1-BB-A51 01(a)(b)B _ Al(c)(p)IA - 28...

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Om2m Scale4m97 -A+B-AA1-2B9A1-BB-A51 01(a)(b)B _ Al(c)(p)IA - 28

Om 2m Scale 4m 97 - A+B -A A 1-2B 9 A 1-B B-A 51 01 (a) (b) B _ Al (c) (p) IA - 28



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In Exercises 11-18, if possible, find (a) $A+B$, (b) $A-B$, (c ) $3A$, and (d) $3A-2B$.

$A = \left[ \begin{array}{r} 1 & -1 & 3 \\ 0 & 6 & 9 \end{array} \right]$, $B = \left[ \begin{array}{r} -2 & 0 & -5 \\ -3 & 4 & -7 \end{array} \right]$

Now we're here. We've been given to mattresses. Okay, so in the first part, we've been asked to find out a plus B. So how do you find out? A plus B? Simply for that. What we'll do is we'll just add of the respective elements, as in what I'm trying to say is if you just take up the first element, I mean the first element off the element of first ruined. First, call them off Patrick's aid, then you'll take the same element. That is the element off the first. True. I'm first column off metrics be as well. So that makes four plus one. That is five. Then I'm talking about this one now five plus zero, that will give you five again, right? Similarly minus one and minus two. If you just add it up, you'll get minus two. So what I'm doing over here? I'm just adding of the respective elements, the corresponding elements rather you can see right. So this is a matter tricks A plus B, right. This is in front. Off you now, Coming onto the second part, we've been asked to find out a minus B. Okay. This is just the same thing. You just have to subscribe the corresponding elements. Now, In the previous part, we were adding up. Now we'll just subtract. So what we'll do now? What do you lose? Simply just this four on one from this biometrics. So four minus one That will give you three, then five minus zero. That will give you five again, then minus one on minus one. So minus one minus minus one. Practice minus one. President. So you will get to you. Okay. So similarly, Just surprised the corresponding elements on you'll get the metrics a minus. Be. So this is the metrics. A minus, bi now. Okay, coming onto the sea part. Now what we're supposed to find over here is 38 So three over here is nothing but a scaler quantity. So I'm just multiplying the whole mattress A by a scaler quantity three over here. So just multiply each and every element off Patrick's day with three. That means four times three. That is 12 again. Five times three. That is 15. Alright. Minus one times three is minus three. So I'm just multiplying each and every element by three over here. So this is what we call it scaler. Multiplication. So this is the man clicks 38 that is in front. Off you coming on to the last part. We were supposed to find out three a minus, Toby. So C three minus Toby This matter tricks. Uh, three years is in front. Off you. We already know. 38 Andi minus to B c. Toby's again. What? You just multiply the metrics Be this one by the scaler quantity to so on. Multiple nine, uh, toe the metrics p by two. Or you'll get simply, um OK, I'll just write the mattress. Be to be first. So I'm writing the metrics to be over here. Okay, so you'll get to then minus 12. See what I'm doing. Answers multiplying each and every element off the metrics Be by two. So just a moment. Yeah, So yeah, we go under third element. No. So minus one day you'll get minus two over here. Then again to this will remain zero, then four minus six. Act minus seven times. You will give you minus 40. So this is my tricks to be now three a man is to be again the same thing. I'm just going to take the mattress, freeing and Toby and subtract the corresponding elements. So what? I'm going to get a see what you'll do. 12 minus two. That iss 10 7 straightening. See in such kind of cases? No, the spine of the mattresses force. Just multiply the mattress by this killer quantity, and then do the respective additional subtraction. Whatever is being asked over here. So minus 10. Then again, I'm getting minus 10 over here. This is three. And the last treatment that is zero minus minus 14. So that will give you a positive. So this is a metric 38 minus two week. So this is how you apply. You do the following operations.

In this problem. There are four separate parts for A, B, C and D. The first part of the problem is asking us to add to major cities together to add matrix a plus matrix B and the way in which we're going to do that because we're going to create matrix that is the same number rose three rows and same number of columns. Two columns. I want to do so by adding the first number of a to the first number of B we do that wouldn't put that value here. So this is going to be a plus one. Then I'm going to the same for the next value. Negative one and negative six. Who was your negative one plus six? We're going to follow through with the rest of the Matrix, and then we're going to write in the value so eight plus one get us nine negative one plus six B five two plus a negative one would be the same thing as saying to minus one, and that would just be one three plus negative. Five is going to be negative to get a four plus one negative three and five plus 10 will get us 15. And this is the Aesir to the question matrix A plus Matrix B Now in part B, we have matrix a minus matrix speed, and we're going to do this in a similar fashion. So we're going to have eight minus one, which is seven negative, one minus six negative, seven to minus and negative one just the same. A saying two plus negative one. What is two plus one? I'm sorry. We had to three and three minus and negative five, which would get us eight pieces. Same thing as saying three plus five. They get a four minus one will be negative. Five and five minus 10 will be negative. Five. And so this is he Answer it to the matrix problem A minus B. Over here we have a similar problem called three times a day. So we don't need to be matrix because it's not anywhere in the question. And right here this number is three is called scaler, which means that you just multiply every number in a by this value. So we're going to end up with the Matrix with the same number of columns and rows as matrix A. So be three times eight. Three times I get of one three times two, three times three returned figure four in three times five and this is going to equal 24. Negative. Three, six, nine *** 12 and 15. And this is going to be the matrix three A. No, her part D it wants to know what three a minus two b is. We already know what 3 a.m. The previous problems. So let's begin solving for to be so will be the same thing you're saying two times one two times six, two times negative. One Two times I get a five, two times one and two times 10. This is going to be to be so we go back to the previous problem. We see that a is equal to 24 three. No, you're 369 Now you're 12 and 15. So if we go over here and write that you have three a is 24 I give three six nine. Now you're 12 and 15 and they want to know what three a minus to be so minus two. So about that minus minus to be so, so, so, so sorry. Minus sir. Two. 12. No, you're too. You give 10 two and 20 and this value is going to be 22. Negative. Three minus negative. 12. So I might as well was going be negative. 15 eight, 19. Negative. 14 and negative five.

The question here gives us two different major, sees A and B and asks us to solve a series of questions. So the first of sub set of this question in part a states that it wants us to add The two major sees together. So we know that, um, through some of the properties of major season, has the same number of corresponding entries weaken, basically, just add them together. So in this particular place, a plus B is equivalent of doing one plus two by taking the first of each and then doing the same with Second, um, second row, first column, negative one plus negative one ah, two plus negative one. And, of course, negative one plus eight. So from here, we can state that it is equal to three one negative two and seven. So that would be the major extents obtained by doing a plus B for, um part beat. It states that we want to subtract it, and by that we know we can do the same thing here. So one minus two. Um, negative one minus negative. 12 minus negative one and negative one minus eight. So from here, we get negative 10 three and negative nine as such. So that would be the answer to this matrix here. I'm see states that it wants us to do a scaler times the matrix of A from here through the property of scaler multiplication. We know that we have to generally just do that if we put it as this. Rather, we can just multiply each single corresponding entry within the Matrix with the numerical value of three. And that would give us the scaler off such. So they'll be just, um three negative 36 and negative three as such. So the last sub part of this question us us to do three a minus to be minds to be so essentially if we use the first section here on 36 negative three negative three. And we subtract that with two times the value of all the corresponding entries in be I give 18 which is the same thing is of course, if we write that down like so, um, we would get minus four negative too negative, too. And 16. So if we basically just subtract both of these together, we would get the value of negative one um, negative one. Of course. Three plus two. I'm six plus two is of course, no one rather than be eight and then negative 19. So that would be the value of this matrix here. So those would be all four answers to the four subsets in this question.

The first part of this problem asks us to add the two Major sees A and B In order to do that, we must find this value of matrix a plus this value of matrix B and do that for all the values following. So negative born plus negative three is going to be in negative for four plus five is nine and zero plus one is when you want and we're going to do if the rest of the problem so five negative six negative five 15 Negative. Five negative too. Three, 10 negative. 10 negative four zero And negative too. And we get this matrix right here. Bobby, we're doing a similar thing. Except for instead of adding these two values were going to be subtracted them. So negative one minus and negative three. It is she going to be negative one plus three. And so that is going to be too. Four minus five is negative. One and zero minus one is also negative One. Now, we're going to finish this for this of this part of the problem, and we're going to get this matrix right here. Part C is a little bit different in the fact that we're going to use this number up front, call this killer and we're going to multiply each value in a by three. So we're going to get three times. They could have won three times four, three times, zero three times three, three times Negative, 23 times two and so on. For the rest of this part C of the problem. We're going to end up with this matrix right here. We're going to use this matrix important to you the problem where it says three times a day. It's the same thing as it's right here. It's the first step of this problem is multiplying to buy every number in B. And so we have this matrix here. My tricks three a. Which we're just going to take that and drawn a will bring it down and minus so too times negative three is going to be negative. Six. We have 10 and two four negative eight negative. 14 and so on. We're gonna get this matrix, which you're going to call to be, And the answer that the problem wants is what we get when we get three a minus to be. So when you take each of the numbers from this matrix up here and to track them from the corresponding number by the corresponding number and to be so we have negative three minus and negative six. That's going to be the same thing as saying three plus six. I'm negative three plus six. So we're going to get three. 12. Minus 10 is 20 Minus two is negative, too. Were ones is for each of the rose in the party of the problem. Nine minus four is five negative, six minus and negative. Eight is going to be too six minus and negative. 14 is going to be eight. Oh, sorry is not going to He's going to be 20 because it's six plus 14. 15 minus 20 is going to be negative. Five 12 minus negative. 18 Is going to be 30. Negative. Three minus and negative, too, is going to be negative. One zero minus six Negative. 6 24 minus four is just 20 negative. 18 months and negative. Eight is only negative. 10. 12 year 12 minus zero is still night of 12. Negative. Three of minus two is bring the negative five and zero minus and I get a four is the same thing as saying zero plus four. So it's just going to be for and this is the matrix you want to get when you finish part D.


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