Question

Solve for the matrix X if 6(5XA-C)^(-1)XD=-5B

Answer 1

Answer the solution for the matrix XX is:

X=−56(5XA−C)BD−1X=−65​(5XA−C)BD−1

Step-by-step explanation:To solve for the matrix XX in the equation 6(5XA−C)−1XD=−5B6(5XA−C)−1XD=−5B, we'll isolate XX step by step.

Given:

6(5XA−C)−1XD=−5B6(5XA−C)−1XD=−5B

Step 1: Multiply both sides by the inverse of 6(5XA−C)6(5XA−C):

(5XA−C)−1XD=−56B(5XA−C)−1XD=−65​B

Step 2: Multiply both sides by the inverse of DD from the right:

(5XA−C)−1X=−56BD−1(5XA−C)−1X=−65​BD−1

Step 3: Multiply both sides by the inverse of (5XA−C)−1(5XA−C)−1 from the left:

X=−56(5XA−C)BD−1X=−65​(5XA−C)BD−1

So, the solution for the matrix XX is:

X=−56(5XA−C)BD−1X=−65​(5XA−C)BD−1