Solve the Matrix Equation [[-1,-2],[4,8]]+X=[[-5,-1],[2,1]]

$[\begin{array}{c} - 1 & - 2 \\ 4 & 8 \end{array}] + X = [\begin{array}{c} - 5 & - 1 \\ 2 & 1 \end{array}]$

Step 1

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

Subtract $[\begin{array}{c} - 1 & - 2 \\ 4 & 8 \end{array}]$ from both sides of the equation.

$X = [\begin{array}{c} - 5 & - 1 \\ 2 & 1 \end{array}] - [\begin{array}{c} - 1 & - 2 \\ 4 & 8 \end{array}]$

Step 2

Simplify the right side.

Subtract the corresponding elements.

$X = [\begin{array}{c} - 5 + 1 & - 1 + 2 \\ 2 - 4 & 1 - 8 \end{array}]$

Simplify each element.

Add $- 5$ and $1$ .

$X = [\begin{array}{c} - 4 & - 1 + 2 \\ 2 - 4 & 1 - 8 \end{array}]$

Add $- 1$ and $2$ .

$X = [\begin{array}{c} - 4 & 1 \\ 2 - 4 & 1 - 8 \end{array}]$

Subtract $4$ from $2$ .

$X = [\begin{array}{c} - 4 & 1 \\ - 2 & 1 - 8 \end{array}]$

Subtract $8$ from $1$ .

$X = [\begin{array}{c} - 4 & 1 \\ - 2 & - 7 \end{array}]$