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 Subtraction
• Matrix Multiplication

## How to Solve Matrix Equations?

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

### Cramers Rule

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