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

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=−65B
Step 2: Multiply both sides by the inverse of DD from the right:
(5XA−C)−1X=−56BD−1(5XA−C)−1X=−65BD−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