Solve the Matrix Equation x-[[1,3],[-1,5]]=[[4,-1],[2,3]]

$x - [\begin{array}{c} 1 & 3 \\ - 1 & 5 \end{array}] = [\begin{array}{c} 4 & - 1 \\ 2 & 3 \end{array}]$

Step 1

Move all terms not containing a variable to the right side.

Add $[\begin{array}{c} 1 & 3 \\ - 1 & 5 \end{array}]$ to both sides of the equation.

$x = [\begin{array}{c} 4 & - 1 \\ 2 & 3 \end{array}] + [\begin{array}{c} 1 & 3 \\ - 1 & 5 \end{array}]$

Step 2

Simplify the right side.

Add the corresponding elements.

$x = [\begin{array}{c} 4 + 1 & - 1 + 3 \\ 2 - 1 & 3 + 5 \end{array}]$

Simplify each element.

Add $4$ and $1$ .

$x = [\begin{array}{c} 5 & - 1 + 3 \\ 2 - 1 & 3 + 5 \end{array}]$

Add $- 1$ and $3$ .

$x = [\begin{array}{c} 5 & 2 \\ 2 - 1 & 3 + 5 \end{array}]$

Subtract $1$ from $2$ .

$x = [\begin{array}{c} 5 & 2 \\ 1 & 3 + 5 \end{array}]$

Add $3$ and $5$ .

$x = [\begin{array}{c} 5 & 2 \\ 1 & 8 \end{array}]$