Final answer:
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]].