Solve the Matrix Equation [[7,-2,5],[11,0,-4]]+x=[[6,-2,13],[8,5,-4]]

$[\begin{array}{c} 7 & - 2 & 5 \\ 11 & 0 & - 4 \end{array}] + x = [\begin{array}{c} 6 & - 2 & 13 \\ 8 & 5 & - 4 \end{array}]$

Step 1

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

Subtract $[\begin{array}{c} 7 & - 2 & 5 \\ 11 & 0 & - 4 \end{array}]$ from both sides of the equation.

$x = [\begin{array}{c} 6 & - 2 & 13 \\ 8 & 5 & - 4 \end{array}] - [\begin{array}{c} 7 & - 2 & 5 \\ 11 & 0 & - 4 \end{array}]$

Step 2

Simplify the right side.

Subtract the corresponding elements.

$x = [\begin{array}{c} 6 - 7 & - 2 + 2 & 13 - 5 \\ 8 - 11 & 5 - 0 & - 4 + 4 \end{array}]$

Simplify each element.

Subtract $7$ from $6$ .

$x = [\begin{array}{c} - 1 & - 2 + 2 & 13 - 5 \\ 8 - 11 & 5 - 0 & - 4 + 4 \end{array}]$

Add $- 2$ and $2$ .

$x = [\begin{array}{c} - 1 & 0 & 13 - 5 \\ 8 - 11 & 5 - 0 & - 4 + 4 \end{array}]$

Subtract $5$ from $13$ .

$x = [\begin{array}{c} - 1 & 0 & 8 \\ 8 - 11 & 5 - 0 & - 4 + 4 \end{array}]$

Subtract $11$ from $8$ .

$x = [\begin{array}{c} - 1 & 0 & 8 \\ - 3 & 5 - 0 & - 4 + 4 \end{array}]$

Subtract $0$ from $5$ .

$x = [\begin{array}{c} - 1 & 0 & 8 \\ - 3 & 5 & - 4 + 4 \end{array}]$

Add $- 4$ and $4$ .

$x = [\begin{array}{c} - 1 & 0 & 8 \\ - 3 & 5 & 0 \end{array}]$