Solve the Matrix Equation x+[[-12,15],[15,6]]=[[2,8],[1,3]]

$x + [\begin{array}{c} - 12 & 15 \\ 15 & 6 \end{array}] = [\begin{array}{c} 2 & 8 \\ 1 & 3 \end{array}]$

Step 1

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

Subtract $[\begin{array}{c} - 12 & 15 \\ 15 & 6 \end{array}]$ from both sides of the equation.

$x = [\begin{array}{c} 2 & 8 \\ 1 & 3 \end{array}] - [\begin{array}{c} - 12 & 15 \\ 15 & 6 \end{array}]$

Step 2

Simplify the right side.

Subtract the corresponding elements.

$x = [\begin{array}{c} 2 + 12 & 8 - 15 \\ 1 - 15 & 3 - 6 \end{array}]$

Simplify each element.

Add $2$ and $12$ .

$x = [\begin{array}{c} 14 & 8 - 15 \\ 1 - 15 & 3 - 6 \end{array}]$

Subtract $15$ from $8$ .

$x = [\begin{array}{c} 14 & - 7 \\ 1 - 15 & 3 - 6 \end{array}]$

Subtract $15$ from $1$ .

$x = [\begin{array}{c} 14 & - 7 \\ - 14 & 3 - 6 \end{array}]$

Subtract $6$ from $3$ .

$x = [\begin{array}{c} 14 & - 7 \\ - 14 & - 3 \end{array}]$