Solve the Matrix Equation [[-3,-7],[1,9]]+x=[[-3,4],[6,5]]

$[\begin{array}{c} - 3 & - 7 \\ 1 & 9 \end{array}] + x = [\begin{array}{c} - 3 & 4 \\ 6 & 5 \end{array}]$

Step 1

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

Subtract $[\begin{array}{c} - 3 & - 7 \\ 1 & 9 \end{array}]$ from both sides of the equation.

$x = [\begin{array}{c} - 3 & 4 \\ 6 & 5 \end{array}] - [\begin{array}{c} - 3 & - 7 \\ 1 & 9 \end{array}]$

Step 2

Simplify the right side.

Subtract the corresponding elements.

$x = [\begin{array}{c} - 3 + 3 & 4 + 7 \\ 6 - 1 & 5 - 9 \end{array}]$

Simplify each element.

Add $- 3$ and $3$ .

$x = [\begin{array}{c} 0 & 4 + 7 \\ 6 - 1 & 5 - 9 \end{array}]$

Add $4$ and $7$ .

$x = [\begin{array}{c} 0 & 11 \\ 6 - 1 & 5 - 9 \end{array}]$

Subtract $1$ from $6$ .

$x = [\begin{array}{c} 0 & 11 \\ 5 & 5 - 9 \end{array}]$

Subtract $9$ from $5$ .

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