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Previous ProblemProblem ListNext Problempoint) A and B are 4 X 9 matrices, and C is a 8 X 4 matrix, which of the following are defined?A CT B. AT cT C. B-A D. C + A...

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Previous ProblemProblem ListNext Problempoint) A and B are 4 X 9 matrices, and C is a 8 X 4 matrix, which of the following are defined?A CT B. AT cT C. B-A D. C + A E. AC E CB

Previous Problem Problem List Next Problem point) A and B are 4 X 9 matrices, and C is a 8 X 4 matrix, which of the following are defined? A CT B. AT cT C. B-A D. C + A E. AC E CB



Answers

If $A_{2 \times 3}, B_{4 \times 3}$ and $C_{2 x 4}$ are three matrices, then which of the following is/are defined? (1) $\mathrm{AC}^{\mathrm{T}} \mathrm{B}$ (2) $\quad \mathrm{B}^{\mathrm{T}} \mathrm{C}^{\mathrm{T}} \mathrm{A}$ (3) $\mathrm{AB}^{\mathrm{T}} \mathrm{C}$ (4) All the above

In the problem is equal to me, B a b is equal to c d d c. No A B is given us a b b A and to c d D C. So this is equal to a C plus B D 80 plus B C. Be simples. Eddie, B D plus sc no B equals c D d C into a b B A. This equals two. Is he blessed deedee, B C plus D A 80 plus busy B. D plus jesse. That is equal to baby. Therefore we can say that B is equal to maybe this is the answer.

To solve this system, I'm first going to switch our bottom two equations, so our order will now be for a plus nine. B equals eight six B plus six C equals negative one and ate a plus six C equals negative one. Now I'm going to rewrite all of these equations so that all of our variables lineup so again for a plus nine b. And since this equation doesn't have a C term, we're gonna just leave a gap equals eight. We're gonna leave a gap over here where the a term would be We're gonna go six b plus six c equals negative one, and then our last equation will be eight A. This does not have a B term. So I'm elated. Gap here plus six c equals negative one. So next I'm going to write this as a matrix and remind you that to do this you just go ahead and we take all our variables out. So all of our information will go into brackets and it will read as four nine. We leave a zero where we don't have a an entry and then eight zero. Since there was no a term six six negative one and then our bottom row will read eight zero since there was no term there. Six and negative one. Now, since our first column in row two already has zero, we can go ahead and bypassed this one and we will multiply our top row by negative too, so that our top row and our bottom row will cancel up. So we're going to be finding our new values for our third row. So this will be negative. Eight negative, 18 zero Negative. 16. Since we weren't doing anything to our second row, our second role remain the same. Zero, six, six, negative one. And since our third row is the one that we're finding new values for, it would also remain the same Positive eight zero six and negative one. Now, to find our new values for our third World, we're gonna go ahead and we're going to add the first and the third rose together. So our two eights will cancel out negative eight plus positive 80 This will be a negative 18 and this would be a positive six. Negative. 16 plus negative one is negative. 17. And so now this becomes our new Row three. So our matrix should now look like this. Our first road will go back to normal for nine zero AIDS. Second row is the same. 066 negative one in our new bottom row will be zero negative, 18 six and negative 17. At this point, we still need for our second column of Row three to be a zero. And so to do this we will be multiplying our second row by three. So our first role will be the same for nine zero, eight zero, six times 3 18 18. Negative three nor bottom row is the same. Zero negative, 18 six. Negative 17 now like we did before. We're going to add our second and third rows together so that we can get our final third row answer. So 18 minus 18 this is going to be zero 18 plus 16 is 24 and negative. Three minus 17 is negative. 20. And so now we can go ahead and input that as our final third row answer. So now our matrix should read for nine. Zero eight zero 18. 18. Negative. Three. Our third row. Zero zero. 24 20. Negative. 20 And at this point, since our second column of our third row is a zero, we can go ahead and add all of our variables back. So we have four. A plus nine b equals eight. 18 d plus 18 c equals negative three and 24 see equals negative 20. Now we can solve for C divide both sides by 24 and we have C equals negative five over sex. We can input this value for C into the equation directly above it. So 18 be plus 18. Well, an input. Our answer for C negative 5/6 equals negative three. So we have 18. B minus 15 equals three negative thing. You have 15 to both sides so we can get our variable. By itself, 18 b equals positive 12. Divide both sides by 18 and we have that be is equal to 2/3 now, like we did before. Go ahead and input this value into our top equation. And that equation is for a plus nine. B equals eight. So for a we know that our B value is 2/3 equals eight for a nine times to over three is equal to six equals AIDS. Subtract six from both sides so that we can get are variable by itself. And we will have for a equals to divide both sides by force of the A's all by itself. And we have the A equals 1/2. So the answer to this system is 1/2 2/3 and negative 5/6.

The equations given here for a plus nine b is equal to eight eight. A plus 16 is equal to minus one six b si is equal to minus one. No, here every question might seem tohave moving evens. But over on the set of equations consist three video. So when the right questions and metrics for Benito take into account all three variables No, For the first rule, we will get the coefficients has four, nine and Siegel, because there is no see Tom here was he for the next rule? We have a zero because there is no B and then six and minus one. Finally, there is no in that herd equation. Zeal 66 and minus one. No, the drawer dotted link to separate the provisions and well done. No, The row operations we have to do to convert this metrics into other wife alone form are the first row operation. We can do it. Road to praying are are to prime. Your photo is equal to twice one minus little. So after doing this, we will get the first road remains seen. The second rule that no become zero 18 minus C 10 17 and the third row will remain the same. Zeal Sick six And buying this one. No, The next row operation. We need to do his own rule three because the second element doctoral three needs to be made Zero. So really, you know, three Prime That is mortal Critical Little minus three times room one. Will he ever get nine states? That is three things through. So, having get four nine you and a little one will remain scene little to no sorry Mean seems 30 18 minus 6 17 and drew a tree even know become Riedel Zito minus drink before and indeed no, we can see that this matrix is now Angelika gone home. So from here from the last rule, we can write the equation minus 24 seen is equal to 20 Therefore C is equal to 20 upon minus 24 That gives us minus five upon sick from the second rule weaken great 18 being minus six things See which is minus for you So this will become 16 minus life by six is equal 17 So from here we get 18 b Bless you We will do 17 therefore B is equal to 70 minus fight that is 12 upon eight. Things of this gives us on three. So this is the value be next begins all from the first group we can write. Any question was all for it. You get for a is equal to 18. No, we can bring the nine be on this side We have minus nine B which is drew upon three that is 18 minus speaks. They gives us two and therefore is equal to two upon four That is therefore we have our answers. He is equal to the heart B is equal to two upon three and sees a golden minus by upon

This motion. Uh, and this is a A and seen. Are you fine? As is a one six minus one. You are this a one seven on this nine and right, Just see on seal. Find this one. I honestly no, you have to get going. Angel shuffling coronets up. You know why? So on observing these Yeah, that metrics is off the dimension wife. Or just piece off the damages one by for democracy is over Dimension What? By what? So is and B c is on a baby. It's can no him flying No on observing. You get that? That this is e B and be he's lying was and just a c is equal on zeal since I list one undivided by or seal when you keep that by one zeal minus one. Oh, here we go again. I just ever did level a series I list you. No, not just a moral people of us. C. Morgan B at this mine honesty Oh, are deployed by one. So my last night only. And your being gay? Is he me? Is it like this? I honesty by Liston Beaver on his own minus six minus minus 14 and being minus No, that's come to the murky, clever Izzy It is, nor define one. So at this BC year be and see me on. Oh, all right.


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