Solve the Matrix Equation [[5,-7],[1,9]]+X=[[4,4],[7,5]]

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

Step 1

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

Subtract $[\begin{array}{c} 5 & - 7 \\ 1 & 9 \end{array}]$ from both sides of the equation.

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

Step 2

Simplify the right side.

Subtract the corresponding elements.

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

Simplify each element.

Subtract $5$ from $4$ .

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

Add $4$ and $7$ .

$X = [\begin{array}{c} - 1 & 11 \\ 7 - 1 & 5 - 9 \end{array}]$

Subtract $1$ from $7$ .

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

Subtract $9$ from $5$ .

$X = [\begin{array}{c} - 1 & 11 \\ 6 & - 4 \end{array}]$