Question

Let A=[[3,-5],[6,4],[-7,6]] and B=[[-8,9],[-6,-8],[7,2]]. Solve the matrix equation 4x+3A=B for x

Answer 1

To solve the matrix equation 4x+3A=B for x, first find the matrix product 3A, then subtract 3A from both sides of the equation, and finally divide both sides by 4 to solve for x.

Step-by-step explanation:

To solve the matrix equation 4x+3A=B for x, we need to isolate x on one side of the equation. First, let's find the matrix product 3A. Multiply each element of matrix A by 3 to get:

A = [[9, -15], [18, 12], [-21, 18]]

Next, subtract 3A from both sides of the equation to isolate 4x:

4x = B - 3A

Substitute the given matrices into the equation:

4x = [[-8, 9], [-6, -8], [7, 2]] - [[9, -15], [18, 12], [-21, 18]]

Simplify the right side of the equation:

4x = [[-17, 24], [-24, -20], [28, -16]]

Finally, divide both sides of the equation by 4 to solve for x:

x = [[-17/4, 24/4], [-24/4, -20/4], [28/4, -16/4]].