Solve for X. [[-9,-7],[0,7]]-X[[3,4],[-2,5]] = I X=??  

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The matrix X has to be determined so that: `[[-9,-7],[0,7]]-X[[3,4],[-2,5]] = [[1,0],[0,1]]`

`[[-9,-7],[0,7]]-X[[3,4],[-2,5]] = [[1,0],[0,1]]`

Let `X = [[a, b],[c,d]]`

=> `[[-9,-7],[0,7]]-[[a, b],[c,d]][[3,4],[-2,5]] = [[1,0],[0,1]]`

=> `[[-9,-7],[0,7]]-[[3a-2b,4a+5b],[3c-2d,4c+5d]] = [[1,0],[0,1]]`

-9 - 3a + 2b = 1, -7 - 4a - 5b = 0 and 2d - 3c = 0, 7 - 4c - 5d = 1

  • 2d - 3c = 0, 7 - 4c - 5d = 1

=> d = (3c)/2

Substitute in 7 - 4c - 5d = 1

7 - 4c - 5(3c)/2 = 1

=> (23/2)c = 6

=> c = 12/23

d = 18/23

  • -9 - 3a + 2b = 1, -7 - 4a - 5b = 0

-9 - 3a + 2b = 1 => a = (2b - 10)/3

Substitute in -7 - 4a - 5b = 0

=> -7 = 4*(2b - 10)/3 + 5b

=> -7 = -40/3 + 8b/3 + 5b

=> 19/3 = 23b/3

=> b = 19/23

a = -64/23

The matrix X is `[[-64/23,19/23],[12/23,18/23]]`

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