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

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

Step 1

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

Add $[\begin{array}{c} 1 & - 1 \\ - 2 & 2 \end{array}]$ to both sides of the equation.

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

Step 2

Simplify the right side.

Add the corresponding elements.

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

Simplify each element.

Add $- 2$ and $1$ .

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

Subtract $1$ from $- 3$ .

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

Subtract $2$ from $2$ .

$x = [\begin{array}{c} - 1 & - 4 \\ 0 & 2 + 2 \end{array}]$

Add $2$ and $2$ .

$x = [\begin{array}{c} - 1 & - 4 \\ 0 & 4 \end{array}]$