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Use the following matrix:-1A =Write the transpose of matrix A.AT...

Question

Use the following matrix:-1A =Write the transpose of matrix A.AT

Use the following matrix: -1 A = Write the transpose of matrix A. AT



Answers

Give a formula for the $i$ jth entry of the transpose of a matrix $A$

In this problem were given an example of a matrix A and it's transposed matrix a T. And it looks like what happened to go from A to a T is just to switch the order of the numbers on the diagonal, the two in the three switched places. So it now our job is to make up a matrix whose transposed is the same thing. So if I make up a matrix that has the same number in both positions on that matrix, then when I switched their order, I'm still going to get to and two in the same place. So it looks the same. So we'll say that that is our example of a transpose that's equivalent to the original.

In this question, we have to evaluate determinant A by expanding across the second column. So this is our second column here. Therefore, the dominant A will be a one do cool factor off 12 plus a to co factor off due to less a three to go factor off three to So therefore, this will be equal to a one comma two is minus food. A photo is zero and 88 with two. So therefore they went to A to be equal to zero. So the storm will get cancelled now in order to find a one comma too. So this is at one comma, two element. We will eliminate these tools so this will be equal to minus four into minus one race part one plus two, which is three to terminate off to one ministry and minus five less go into minus one race Part three plus two, which is five. The dominant gal's. So this is a 32 element here we will eliminate these two rows so the determinant will be seven to minus six and minus three, so this will be equal to minus for into minus one, which is equal to food doing to minus five is minus 10 minus one to minus three, which is minus street. This will be will do two in minus one. So this will be minus two into seven into 72 ministries, minus 21 minus six in tow, minus six. Interview is minus 12. So this is equal to four into minus 10 plus three minus doing too minus 20 ventless. Well, so this is equal to four into minus seven. Minus doing toe minus time. So seven to minus one is minus 28 and 92 and dryness less 18. So this is equal to minus then.

In this question, we have to expand the dominant dates using the third column. So determinate off able beak were to a 123 Cool factor off one tree less a Tucci Cool factor off 23 less a 33 Go back to Ralph G. Three and a 43 cool factor off 43 now a country and a 23 r zero. So therefore, these symptoms will already be zero eight. Treaty is seven. Cool factor off G three and a four tree is minus one, so this will be minus one in Tokyo. Factor off 40. No cool factor off treaty will be equal to minus one DRES Part three plus three, which is six minor off tree tree, and this will be minus one into the cool factor of four. Tree will be minus one days. Part four plus three, which is seven minus 40 now minus one race bar six s plus one. So this would be seven m tree tree on minus one race. Part seven is minus one so minus one into minus one will be less one. So they put. This will be plus one and two M 40 now in order to find the value off em treaty. So this is that 33 element will eliminate these two, so we will get seven times to terminate off one Zito minus two, 410 and minus two minus Trian Zito. This will be one times predominant off. Sorry. Minor off 40. So this is four comma tree element. We will eliminate these two, so we will get 10 minus two, 410 and 568 Since here in the third column, there are already two elements which are zero. There would we will expand using this. So this will be quick to seven into minus to determine it off. Food one minus two, minus three less. This will be the one. Times two dominant off 1068 minus two. Dominant off 415 six. This is seven into minus two, which is minus 14. This will be would do minus 12 minus minus two. This will be up less. One in tow, eight minus zero. This will be minus doing doing before minus five. So this is minus 14 into minus 10. Less eight minus two in tow. 19. So this is 140 bless eight minus doing to 19 which is coming out to be 100 and 10.

In this question, we have to a better determinant d expanding over first rule. So therefore, in the first rule, we will simply write the minor off the respective elements. And we will be using these signs plus minus pleasant minus to write a co factors. So the dominant able we were two plus one into determinate off. We will eliminate these. So we will get one zero a 0678 minus T minus 10 These two terms will be real busy road. So therefore, there's no need off writing the cool factor because their resultant will already with you minus of minus two will be blessed to on when we expand. But he died The miners. We will have to eliminate these two. So the element will be 410 567 minus two minus 60 and minus one. So expanding this we will get the first rule here is already zeros of this will be turned into one and two dominant off 78 minus 10 Unless this will be done So this will begin less minus and less So zero is already the minor and 2030 So will not be writing that down, so this one week will do less food into the dominant off. 67 minus three and minus one. This will be minus one to dominate golf 57 minus two and minus one. So this is coming out to be 7 to 0, which is zero minus minus saved and when the one would be one and doing toe. So this would be minus six minus minus 21 minus wanting to minus five minus minus 14. So this will be eight less doing toe. This will be four and 21 minus six, which is equal to 15 minus one, and this will be 14 minus five. So minus one into nine will be my minus time. So, therefore, for into 15 minus nine, which is equal to 51 51 in tow. Two is equal to 102 and 102 plus eight will be called 210


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