Question

What is the solution of the matrix equation?
[9 4]is the top part of the first matrix, [2 1] is the bottom part of the first matrix. X= is between both matrixes. [-9 -6] is the top part of the second matrix [-1 -8] is the bottom part of the second matrix.

Answer 1

To find the solution of the matrix equation, we need to find the value of X that satisfies the equation:

[9 4] X [-9 -6]
[2 1] = [-1 -8]

The equation can be expanded as follows:

[9x + 2y 4x + y] = [-9 -6]
[-1 -8]

Comparing corresponding elements on both sides of the equation, we get the following system of equations:

9x + 2y = -9 (equation 1)
4x + y = -6 (equation 2)
2x + y = -1 (equation 3)
x + 8y = -8 (equation 4)

We can solve this system of equations using various methods such as substitution or elimination. Let's solve it using the elimination method:

From equations 2 and 3, we can eliminate y by subtracting equation 2 from equation 3:
(2x + y) - (4x + y) = -1 - (-6)
-2x = 5
x = -5/2

Substituting x = -5/2 into equation 3:
2(-5/2) + y = -1
-5 + y = -1
y = 4

So, the solution to the matrix equation is:
X = [-5/2 4]