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Assume that A and Bare 3 X 3 matricesIndicate which of the following are true. (Select ALL that are true:)(A(3A + SB)) SBT A + 3AA:OA' B' (BA)A' Ais ...

Question

Assume that A and Bare 3 X 3 matricesIndicate which of the following are true. (Select ALL that are true:)(A(3A + SB)) SBT A + 3AA:OA' B' (BA)A' Ais 3 symmetric matrix

Assume that A and Bare 3 X 3 matrices Indicate which of the following are true. (Select ALL that are true:) (A(3A + SB)) SBT A + 3AA: OA' B' (BA) A' Ais 3 symmetric matrix



Answers

If $A$ and $B$ are symmetric matrices and $A B=B A$, then $A^{-1} B$ is a (A) symmetric matrix (B) skew-symmetric matrix (C) identity matrix (D) None of these

So for this question, we want to prove that for any free by free matrix. If it has a to rows or columns are identical, then the determinant is equal to zero. So just proved by example, we'll just start the matrix one to free, then also have 111 111 as our second inferred wear. So to find the determinant off, this matrix really used the first very just because it wouldn't matter what very rich or column a Chiuso a class minus plus. So it finding the minor determinant off the first positive one, we would be finding it. Determine off one one on one minus two lots off one on 11 plus three lots off 1111 It's one times one minus one. It's obviously they were minus two dots of zemarai last three lots of zero. So I determined it off. This matrix is therefore there were

All right, so if we have some three by three matrix A B c D e f G h I is a three by three matrix, we'll call this be The transpose is a d G. They a age c f I so b plus be transposed is to a B plus D C plus G d plus de to e plus h g plus C H plus F and two I. So what, we'll call this matrix magic see on we're going to note that C is equal to see transpose because B D plus B z B plus t G policies equal the sequence. G H plus F is equal to half plus age so cuz equal to see transposed.

Let a matrix three close that is stool minus one. Judo 15 minus one. And my picks will be one. Go to the judo. Do minus one. Judo 45 into so fresh. Find the detriment off people. Be so first, find a place to be This is a quarto Combine the got us Wyndham's which is three for cool. Gee, it'll slave 37 on a the settlement off a plus B, which is three for two. Do judo five today one poor if you kill collected. It's this acquittal three times Geo minus 35. My next four times eight minus 15 plus two times 14 minus. So this is my s 105 bless 28 and plus 20. So finally cooperating this so find the sick little minus 40. No more or less of a so you can clip more or less A a means that it went up eight which is equal to minus one to go minus one Judah 15 and minus one. Hope minus one. Go for So calculating this through times for minus then minus two Digital plus five minus one doodle blessed one. This is a quarto minus 12 minus 10 on minus one, which is acquittal minus 23 morning. But it's killing 123 one Go three to minus one Geo 45 four, five Jiro, another scalpel. It one judo minus Tito minus store general minus Tito and plus three minus four minus day. So all the June issue portal. So finally, the scalpel it that blessed be equal are not so a plus B. Work hard pitch this. This is minus 49. This is minus more A which is minus 23 on this minus 40. So combining this this minus 49 this is minus 56 so both are not equal.

So in the given question, we are told that we have a matrix A We have a matrix game which is off the order three by two. Right. And we have to find what kind of metrics we can get With eight times 8 transports. So what we have as options is eight times 8 transports would be and narrow metrics. It would be a diagonal that drinks and I am going to the electrics. It is an identity matrix or of Cindy, which says it is a symmetric metrics. So we should find which of these options is correct. Right? So what we can do over here is we know the order of a. Right? So, since we know the order of a let's Big A metrics eight in which we have three rows and two columns. Right? So let's Right that assume yes, equal to a B Cd here, that is some interests with three rows and two columns. Then a transports would be equal to E b d F. Right? So, now let's take the product of A and transport. So eight times 8 transports would then be equal to when we take the product of these two matrices. What we object is A squared plus B squared, A C plus baby, A plus B F, A C plus B, D C squared plus B squared C E plus deer, E. Place for BF, C E Bless dear. And he squared plus X squared. So this is what we get as the product of eight times eight transports. Right? So from this, We can say that the Matrix eight times were transposed is not a narrow metrics, right? It is not equal to zero. And we can also say that it is not our diagonal matrix also. Right? So we can see this and we can also say that eight times they transpose is not the identity matrix. And this is what we are left with. Right? So now what we can do is we can take the transports of those metrics and check whether it is symmetric or not. Right? So when we take the transport of eight times their transport, we again get the same metrics which is a square must be square, A C plus V D E plus a fetus, beer, A C plus B D C squared plus the square C E L S D F. And the third columnist E plus BF C E plus deer. He squared plus X squared. So you can see that eight times a transport is the same as the transpose of eight times 8 transports, which means The Matrix formed by eight times a transport as a symmetric metrics. So the option in the question that that uses this answered is option deal sole option B Eight times he transports as the symmetric as the required solution for this sequence for this question. So, I hope you understood the mets are thank you.


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