Solve the Matrix Equation X-[[2,-7],[6,1]]=[[-9,5],[1,-1]]

$X - [\begin{array}{c} 2 & - 7 \\ 6 & 1 \end{array}] = [\begin{array}{c} - 9 & 5 \\ 1 & - 1 \end{array}]$

Step 1

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

Add $[\begin{array}{c} 2 & - 7 \\ 6 & 1 \end{array}]$ to both sides of the equation.

$X = [\begin{array}{c} - 9 & 5 \\ 1 & - 1 \end{array}] + [\begin{array}{c} 2 & - 7 \\ 6 & 1 \end{array}]$

Step 2

Simplify the right side.

Add the corresponding elements.

$X = [\begin{array}{c} - 9 + 2 & 5 - 7 \\ 1 + 6 & - 1 + 1 \end{array}]$

Simplify each element.

Add $- 9$ and $2$ .

$X = [\begin{array}{c} - 7 & 5 - 7 \\ 1 + 6 & - 1 + 1 \end{array}]$

Subtract $7$ from $5$ .

$X = [\begin{array}{c} - 7 & - 2 \\ 1 + 6 & - 1 + 1 \end{array}]$

Add $1$ and $6$ .

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

Add $- 1$ and $1$ .

$X = [\begin{array}{c} - 7 & - 2 \\ 7 & 0 \end{array}]$