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Chapter 2 Matrices 72matrices A_ B, C shown, compute Exercises 23-30. For the when defined, and give a reason for the matrir expressions; failure when not definedB ...

Question

Chapter 2 Matrices 72matrices A_ B, C shown, compute Exercises 23-30. For the when defined, and give a reason for the matrir expressions; failure when not definedB =%C23. AB BA 24. A(BC) , (AB)C 25. BC, CB 26. AAT, ATA 27. BBT BTB 28. ccT , CTc 29. (BCJA , (BC) (BC) 30. (BC)TA, A(BC)T

Chapter 2 Matrices 72 matrices A_ B, C shown, compute Exercises 23-30. For the when defined, and give a reason for the matrir expressions; failure when not defined B = % C 23. AB BA 24. A(BC) , (AB)C 25. BC, CB 26. AAT, ATA 27. BBT BTB 28. ccT , CTc 29. (BCJA , (BC) (BC) 30. (BC)TA, A(BC)T



Answers

For the given matrices $A$ and $B$, evaluate (if defined) the expressions ( $a$ ) $A B,$ ( $b$ ) $3 B-2 A$, and (c) $B A$. For any expression that is not defined, state the reason. $$A=\left[\begin{array}{rr}0 & 4 \\-6 & 7\end{array}\right] ; \quad B=\left[\begin{array}{ll}3 & -7 \\2 & -1\end{array}\right]$$

In this question, we are required to check whether the given expression that is he plus me is defined or not and appears. Then we have to find the result. Now here Matrix A is given to be 0 3 -5, 126 And Matrix B has given us 410 -2 3 -2. First of all, no data order of Matrix A is to cross three and the order of matrix P. S. Also to cross three. Therefore the some A plus B will be defined, and this will be given by the first element will become zero plus four, Then 3-plus 1 -5000, Then 1 -2, two plus three And 6 -2. On simplification, the matrix becomes four four minus five minus one, five and four. This will be the final answer.

Okay. Looking good needs to make. Cease on. We want to find 83 months to a B s. So first off we'll do a B. So it would be too much matrix because we're multiplying to two by two major seats on you have to take for each corresponding out, Theo Corresponding road from the first matrix on column from the 2nd 1 So, for example, first breakfast column would be fast rope against the color. Nine times four is 36 minus four times minus seven is gonna be positive. 28 on their 28 to 36. Well, that's going to be equal to 64. Okay, 60 fours, in your estimation, on its 1st 2nd column, Zeros that nine minus four lots that fires minus 20. Newmont are second road out seven lots of about four. And there might be three blocks that my seven Serie we're gonna have total off. Seven. Lots of seven, which I hate on. Then finally, second road second columns were lots that seven minus three locks that five minus 15 on. This is our a big okay now on. Except you need to you three B minus two and so under constant threat of our matrix, you just time to every single one of the elements by our constant cross. Refer to this as a scaler, say three times that force 12 times anything is zero minus seven times three minus 21 on the 53 50. Equally for are a matrix We've got to us off 9 18 Do not scoff. 4827 is 42 lattes minor, straight past minus six on. But we're doing a possible minus matrix operation. You just do each element the operation with corresponding element in your nature. So, for example, the first row first column just 12 minus 18 which give you my six next up because you're a minus, minus eight second Rhodes College 1st 2nd rate. My 21 minus 17 months. 21 of my 70. You should end up months 38 on. And finally, we've got our 2nd 2nd row, second collar. You've got 21 lots of eggs. You've got months. An A minus on. Then you're gonna minus six lots off. 15 from that. And that should just come out back to 78. Okay, not only we've got our be a three. So this time be says, we're taking the roads big and in the column today. So first row, first column, bathroom big. It's best card. Just got full. What's that? Nice to be fair to six. Uh, next for, uh, get your first round of second column. Zeros that honest? Uh, sir. First, right against second color You've got arthritis from. I'm sorry. You've got because here you've got first broke it, then you've got birthrate. Get set color for lots of likes for my 16th. Sorry. Got a bit of confusion there. Uh, Okay, now, So even onto the second road for big second with minus 75 against 97 minus seven lots off nine. And then you're gonna have seven lakhs. If I'd say you've got minus nine lots is seven years, we can say five or six minutes, minus four lots of seven, which ah, Hignett is equal to minus 28. So get, uh here. We had my 75 against 97 So you end up with a net off minus 47 Okay. And and so we've got the second row second column minus seven lots off minus four, which is 28 on. We've got five of my three minus 15. Which shift? Leave us at 13. So our final trip stay six months. 16 might create 13 on These are our three result in major cities.

Okay, so given to Major sees it. And we want to find a B three B minus two es and then B A if he's possible. So they're supposed to meet its multiplication on modifications. Be possible. The amount of columns in the first Matrix at this case, too, because Cesar First Matrix needs to equal the amount of Rose in our second matrix, which in this case is too intent to line up. So it's perfectly possible to do this on dhe. The resulting matrix is gonna be a two by one as we take the rose in the 1st 1 in the com from 2nd 1 So if a baby would do it here, it's gonna be a two by one. Matrix on final. Like, say, the first row first column would have to do the first row of the first matrix times by defense. Common seconds matrix equally if we weren't to second row first column. But after the second row against the first column, I say that we've got one. Call him here, but I hope you see one alluding to that. So let's find first, we're against First column. You've got minus four times one sets mean minus four out into tough minus three minus six Says we might instead on. Then you've got the second Roosevelt minus one Lots of wine and zeros. My street. It's just gonna minus one on this is Hey, baby, Next up, we've got some subtraction now. Are we doing additional subtraction with matrices? Well, we actually, we want is the dimensions to be exactly the same. Both major cities, unfortunately here we've got two by 2 to 1, so this is actually possible. So now I've got B times A So this one, we first beer, we first on every second. So the columns amount of columns from be niece equally amount off rose from a few modifications possible on a fortune here one does not equal to. So be a is also not possible. So the only one we can actually do is a B, which is minus 10 minus one

In this cushion. Unseeded. The my place is a the and see are defined as all those that is a is equal to 0.3 1.1 You waiting for 0.9 minus 0.1 zero point. Fools minus 0.7 minus. It'll 0.3 minus zero point flight matrices being equal to one point minus. You know, 0.1 seal minus. You know, 0.5 Siegel point by minus 12 point. And like Chrissy, it will do minus zero point, you know point Seattle bank run 1.1 group point line and minus one by one. No, here you need You'll find the metrics, Bessie, by using the But often can you just So he plays the second metrics and by suing, right, right and has the added burden on display. Sean Bill. No, he plays the second and quite burden again. There's the second metrics by placing on added Burden and Pressler. Second, Burton and I just played Sean Willow. No, we pressed the second metrics and by suing not like at all, press the red button and I despair is shown below on a single second and quite button again That's the second metrics by place in all and in Britain. Invest up second buttoning are displayed. Sean Bill No, and a lot of step for finding a metrics BC repressed RBC and their displays, Sean Will, Does the required operation is performed.


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