Solve the Matrix Equation x-[[2,4],[-5,2]]=[[5,-1],[1,0]]

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

Step 1

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

Add $[\begin{array}{c} 2 & 4 \\ - 5 & 2 \end{array}]$ to both sides of the equation.

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

Step 2

Simplify the right side.

Add the corresponding elements.

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

Simplify each element.

Add $5$ and $2$ .

$x = [\begin{array}{c} 7 & - 1 + 4 \\ 1 - 5 & 0 + 2 \end{array}]$

Add $- 1$ and $4$ .

$x = [\begin{array}{c} 7 & 3 \\ 1 - 5 & 0 + 2 \end{array}]$

Subtract $5$ from $1$ .

$x = [\begin{array}{c} 7 & 3 \\ - 4 & 0 + 2 \end{array}]$

Add $0$ and $2$ .

$x = [\begin{array}{c} 7 & 3 \\ - 4 & 2 \end{array}]$