What is the solution of the matrix equation?

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

1 answer

The matrix equation [9 4; 2 1]X = [-9 -6; -1 -8] can be rewritten as:

9x + 4y = -9
2x + y = -6

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

First, let's multiply the second equation by 4 to make the coefficients of y in both equations equal:

8x + 4y = -24

Now, subtract the first equation from this new equation:

(8x + 4y) - (9x + 4y) = -24 - (-9)

Simplifying:

- x = -15

Now, substitute this value of x back into one of the original equations (let's use the first equation):

9(-15) + 4y = -9

Simplifying:

-135 + 4y = -9

Add 135 to both sides:

4y = -9 + 135

4y = 126

Divide both sides by 4:

y = 31.5

So, the solution to the matrix equation is X = [-15; 31.5]