A matrix equation is an equation in which the variable is a matrix or a vector. The general form of a matrix equation is $A\vec{x}=\vec{b},$ where $A$ is a matrix and $\vec{x}$ and $\vec{b}$ are vectors. Matrix equations are used to rewrite systems of equations by following the steps below.

1. Group the coefficients of the system into matrix $A,$ called the coefficient matrix.
2. Group the variables into vector $\vec{x},$ called the variable matrix.
3. Group the constants into vector $\vec{b},$ called the constant matrix.

Note that before writing a system using matrices, the variables must be written in the same order in all the equations. Further, the constants must be on the right-hand side of their respective equations.