Final answer:
To find X in terms of A and B in the matrix equation XA = B, you need to isolate X by multiplying both sides of the equation by the inverse of A. The solution for X in terms of A and B is X = A^-1B.
Step-by-step explanation:
To find X in terms of A and B in the matrix equation XA = B, you need to isolate X by multiplying both sides of the equation by the inverse of A. Since matrix multiplication is not commutative, you need to be careful when rearranging the equation.
Here are the steps: First, find the inverse of matrix A. Let's call it A-1. Multiply both sides of the equation by A-1 from the left: A-1(XA) = A-1B. Use the associativity property of matrix multiplication to rearrange the equation: (A-1X)A = A-1B.
Since A-1A is the identity matrix I, the equation simplifies to X = A-1B. So, the solution for X in terms of A and B is X = A-1B.