Question

Given the matrix equation:

AX + B = C
Outline the steps for solving this equation.
Step 1:

Answer 1

To solve the matrix equation AX + B = C, first identify the system and dimensions of matrices. Then, isolate X by subtracting B from C and finally multiply by the inverse of A on both sides to solve for X.

Step-by-step explanation:

Steps for Solving the Matrix Equation AX + B = C

To solve the matrix equation AX + B = C, where A, B, and C are matrices and X is the unknown matrix, follow these steps:

1. Identify the system of interest by determining the dimensions of the matrices involved and ensuring that they conform to the requirements for matrix multiplication.
2. Isolate the unknown matrix X by subtracting matrix B from both sides of the equation to get AX = C - B.
3. Once isolated, solve for X by multiplying both sides of the equation by the inverse of matrix A, if it exists, giving X = A-1(C - B).
4. Solve the simultaneous equations for the unknowns, which might involve algebraic steps and matrix multiplication.

Throughout this process, ensure to work carefully to avoid any algebraic errors and to double-check each step for accuracy.