What is the solution of the matrix equation? [9 -5 __ 2 -1] X=[8 5__ -7 1]

Question

Options:

A [ -43 0 __ -7 1]

B [ 9 0 __ -79 -1]

C [-43 0 __-79 -1]

D [ 43 1 __ -79 -1]

Answer 1

Question: What is the solution of the matrix equation? [9 -5 __ 2 -1] X=[8 5__ -7 1] ?

Let A^(-1) be the inverse matrix of A = [9 -5 __ 2 -1]. Then (matrix) multiply both sides of the equation by A^(-1), to give

X = A^(-1) [8 5__ -7 1].

The inverse matrix is A^(-1) = (1/det(A))[-1 5__ -2 9]

and det(A) = 9*(-1) - 2*(-5) = -9 + 10 = 1.

So A^(-1) = [-1 5 __ -2 9]

Then,

X = [-1 5 __ -2 9] [8 5 _ -7 1]

X = [ (-8-35) (-5+5) __ (-16 - 63) (-10 + 9)]

X = [-43 0 __ -79 -1]

Answer: Solution is given by option (C)