In this lesson we will go over how to solve a basic matrix equation such as the following:

These are matrices, not

variables.

Before we do anything we should solve the equation for the unknown matrix X.

Add A to both sides.

Multiply both sides by 1/3, because you will be performing scalar multiplication.

You can plug-in the matrices A and B and solve for the matrix X.

Notice that the same rules that apply to variable equations also apply to matrix equations.

In this example we are using the additive and multiplicative properties of matrix equations.

For this example, let’s assume that the values of matrix A and matrix B are given by the following:

Plug-in values for matrices A and B.

Add A and B together.

Multiply by the scalar 1/3.

The matrix X.