Question

Given the matrices A=[[-3,-3],[2,1]],B=[[5,-2],[3,0]], and C=[[1,-1],[4,-1]], solve for the matrix x in the equation n the equation (x-2B)A=C.

Answer 1

To solve the matrix equation (x - 2B)A = C for x, we first multiply both sides by A's inverse, then compute 2B, and finally add 2B to CA^{-1} to isolate x.

Step-by-step explanation:

To solve for the matrix x in the equation (x - 2B)A = C, we will follow several steps to isolate x. First, we need to understand the given matrices A, B, and C:

• A = [[-3, -3], [2, 1]],
• B = [[5, -2], [3, 0]],
• C = [[1, -1], [4, -1]].

The equation can be rearranged to solve for x:

1. Multiply both sides of the equation by the inverse of matrix A to get rid of A on the left side, thus obtaining (x - 2B) = CA-1.
2. Find 2B by multiplying 2 times matrix B.
3. Add 2B to both sides to isolate x on the left side, which gives us x = CA-1 + 2B.
4. Calculate the inverse of matrix A (A-1) and then multiply it with C to get CA-1.
5. Finally add this product to 2B to find the matrix x.

By following these steps carefully and performing matrix operations, we can find the value of the matrix x that satisfies the given matrix equation.