If in an equation, a variable stands in a matrix form, then that equation is known as matrix equation. We can solve such type of equations using the following operations:

  • Matrix Addition
  • Matrix Subtraction
  • Matrix Multiplication


Here, let us learn how to solve matrix equations with the help of the following examples.

Solved Examples

Question 1: Solve for the matrix Z in Z + $\begin{bmatrix}
5 &2 \\
4 &1
\end{bmatrix}$= $\begin{bmatrix}
7 &4 \\
5 &3
\end{bmatrix}$
Solution:
We have = Z + $\begin{bmatrix}
5 &2 \\
4 &1
\end{bmatrix}$ = $\begin{bmatrix}
7 &4 \\
5 &3
\end{bmatrix}$

Z = $\begin{bmatrix}
7 &4 \\
5 &3
\end{bmatrix}$ - $\begin{bmatrix}
5 &2 \\
4 &1
\end{bmatrix}$

Z = $\begin{bmatrix}
2 &2 \\
1 &2
\end{bmatrix}$

Question 2: If 3 $\begin{bmatrix}
y &4 \\
6 &x-1
\end{bmatrix}$ + $\begin{bmatrix}
3 &-1 \\
1&1
\end{bmatrix}$ = $\begin{bmatrix}
9 &5 \\
4 &2
\end{bmatrix}$, find the value of x and y.
Solution:
We have 3 $\begin{bmatrix}
y &4 \\
6 &x-1
\end{bmatrix}$ + $\begin{bmatrix}
3 &-1 \\
1&1
\end{bmatrix}$ = $\begin{bmatrix}
9 &5 \\
4 &2
\end{bmatrix}$

$\begin{bmatrix}
3y &12 \\
18 &3x-3
\end{bmatrix}$ = $\begin{bmatrix}
9 &5 \\
4 &2
\end{bmatrix}$ - $\begin{bmatrix}
3 &-1 \\
1&1
\end{bmatrix}$
$\begin{bmatrix}
3y &12 \\
18 &3x-3
\end{bmatrix}$ = $\begin{bmatrix}
6 &6 \\
3&1
\end{bmatrix}$

Here, we can easily use matrix equality property.

3y = 6 and 3x-3 =1

y = 2 and x = 4/3