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1.10 points Let A, B be 3x3 matrices with inverses as follows: A: 2 3 5 -6 4 3 7 -1 5 B: 3 1 Compute the following: (a) (AB)^-1 (b) [A^-1B^-1 -1A^-1B]^-1

          1.10 points Let A, B be 3x3 matrices with inverses as follows:
A:
2 3 5
-6 4 3
7 -1 5

B:
3 1

Compute the following:
(a) (AB)^-1
(b) [A^-1B^-1 -1A^-1B]^-1
        
110 points let ab be 3 3 matrices with inverses as follows 2 3 5 2 1 6 4 3 7 1 5 b 3 1 compute the following aab 1 b a 1b 1 1a 1b 1 43234

Added by -Scar L.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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1.10 points Let A, B be 3x3 matrices with inverses as follows: A: 2 3 5 -6 4 3 7 -1 5 B: 3 1 Compute the following: (a) (AB)^-1 (b) [A^-1B^-1 -1A^-1B]^-1
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Transcript

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00:01 In this question, we are given the inverses of the matrices a and b, and we are asked to find a -b -inverse and a -transpose inverse.
00:11 To calculate the formula for calculating a -b -inverse is b -inverse times a -inverse.
00:22 So we just need to multiply the matrices, b -inverse and a -inverse.
00:45 To calculate the product, we need to perform the standard matrix by matrix multiplication, and we will solve.
00:53 First row times the first column will give us 6 plus 0 minus 12.
01:03 First row times the second column is going to give us negative 24 plus 5 minus 6.
01:11 And the first row times the last column is going to be 12 plus 15 minus 3.
01:19 Now let's move on to the next row.
01:21 We need to multiply the second row by the first column.
01:25 To get negative 2 plus 0 minus 4.
01:29 The second row times the second column is going to be 8 plus 4 minus 2.
01:37 The second row times the last column equals to negative 4 plus 12 minus 1.
01:47 Now let's write down the last row.
01:50 We need to multiply the last row by the first column.
01:53 We are going to get 1 plus 0 plus 16.
01:59 Last row times the second column is negative 4 plus 3 plus 8 and the last row times the last column is 2 plus 9 plus 4.
02:17 All right.
02:19 Now let's calculate the entries.
02:21 We are going to get negative 6.
02:24 Negative 30 plus 5 is negative 25.
02:30 12 plus 12 is 24.
02:33 The second row is going to be negative 6.
02:37 10 and 7.
02:42 The last row is going to be 17, 7 and 15.
02:53 So this is an inverse of ab...
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