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A) (10F) Compute the matrix product below, where m is a positive integer_-2b) (20%) Compute the closed form for A" , where T is a positive integer.A =(Hint: wr...

Question

A) (10F) Compute the matrix product below, where m is a positive integer_-2b) (20%) Compute the closed form for A" , where T is a positive integer.A =(Hint: write A as AI + B)

a) (10F) Compute the matrix product below, where m is a positive integer_ -2 b) (20%) Compute the closed form for A" , where T is a positive integer. A = (Hint: write A as AI + B)



Answers

Let $\mathbf{M}=\mathbf{M}_{2,2}$ with inner product $\langle A, B\rangle=\operatorname{tr}\left(B^{T} A\right) .$ Find an orthogonal basis for the orthogonal complement of (a) diagonal matrices, (b) symmetric matrices.

Okay, We have the monstrous A when we want to calculate a three a three Is the multiplication off? Three A. So a three it waas too to yeah, to zero four and walk monte. Thanks. Bye to a little four on once it this boy to is little four. Come on. Which becomes the calculation off for a little 12. Mom once, even by to settle. Cool one. Maybe she calls to gate zero 28 one. But we have a minus three, which is the calculation off three times off. A members in verse is one divided by two months ago by minus zero on the reversal. Yeah. What risk is thes once a good play on the way. This way, too. On this little minus four to want to go buy one divided by two on the mattress is born zero minus four to then they can write to get us Yeah, Guan divided like eight. The calculation off the mattress is one federal minus with four. One second by bon zero minus four To which can be written us I'm one divided by eight. Little minus seven. Divided by two. Yeah, on one. On the last thing is a to minus two A plus I a two equals two 14 a little twins on bomb minus two, multiple by 10 minus four on to loss Bond. The single single Uh huh. It can be returned off is little. A little four minus. Well, boss 10 visual on which reports to one zero four, you know.

Younousse program we have in question off metrics modification. So the left inside because to ah, money picture of two matrix on times a matrix petition by on six different parts and that we don't need to I care about the dimension because off this, both metrics are petitioned. Conform obl e and weaken directly years the metrics multiplication rule. So this is the result from the left hand side, and we know the right inside equals two. Ah, a new matrix, which is also, um, petition to the bite. A pairing. Those partitioned are stepping matrix. We will see that, um, Hicks times a 11 plus a 21 equals zero that gives us X equals two minus a 21 times the numerous off a 11 And we know that. Why? Times a 11 plus a 31 he caused zero gives us why close to minus a 31 times three euros off a 11 and that we are looking for the e 22 So we know that b 22 because two x times a 12 plus A to do I project This result the previous results were pretend for X We have B 22 equals two minus 8 to 1 time say 11 universe times a 12 plus a 22 So this is this other solutions to this problem?

We have the matters a on we want to calculate 833 cause toe a multiple by a multiple by a So it is 31 to run Once he felt why 312 long multiple. Why three? 12 Well, on it it cost too. And the man for eight. Three multiple boy three Juan to one on dit It calls toe for someone 15 Cursi on another on behalf a minus three, which is three times a inverse multiple together. So a inverse, a inverse On 18 years, it cost a inverse waas too. One divided by the terminal, which is training minus two. Multiple boy one minus one, minus two on three, most of them for blanc three. My finest, too. Once a good bye WAM Lina Spawn minus two on three. Multiple by bon. Divided by three minus two. Bomb minus one minus two on three. On it. He calls. So three minus four minus eight. And a man Juan minus one, minus two on three. 11 minus 15. Minus 30. I'm 41. Also, we have a two minus two. A loss. I it costs too. Three, 12 Long. Once again. Why three on to why minus two months of 25. Three. Blonde to Blanc plus one. Siegel, you fun on it. It calls toe 11 4, four eight That three minus thanks to for toe lost. 10 little what? Which he wants to. Six to full True.

This problem we've been given matrix A. Is equal A. B, C. D. And matrix B. There's a Matrix 1001. And we would like to find the value of A. B. And value of B. A. Find A B. This is A. B C. D. Times 1001. We multiply the rose by the columns. We have a plus zero. And that's a. Now if we move over and multiply it by the second column, this will be zero. B is B. Now let's move down. And multiply second role by the first column. B, C plus zero is C. And then the last problem we have zero plus D. Is D. And so this is the matrix A times B. Now that we also want the other way around. So we won't be times A. Just 1001 times A. B C. D. And again we're gonna multiply the row by the calm. And so we have a policy zero which is A. And then we move over. Be paused zero, which is B. Move down zero plus. You would just see we have already have zero plus D. Is deep. My answer here should be A. B. C.


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