Solve the Matrix Equation x-[[2,5],[-5,2]]=[[6,-4],[3,0]]

$x - [\begin{array}{c} 2 & 5 \\ - 5 & 2 \end{array}] = [\begin{array}{c} 6 & - 4 \\ 3 & 0 \end{array}]$

Step 1

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

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

$x = [\begin{array}{c} 6 & - 4 \\ 3 & 0 \end{array}] + [\begin{array}{c} 2 & 5 \\ - 5 & 2 \end{array}]$

Step 2

Simplify the right side.

Add the corresponding elements.

$x = [\begin{array}{c} 6 + 2 & - 4 + 5 \\ 3 - 5 & 0 + 2 \end{array}]$

Simplify each element.

Add $6$ and $2$ .

$x = [\begin{array}{c} 8 & - 4 + 5 \\ 3 - 5 & 0 + 2 \end{array}]$

Add $- 4$ and $5$ .

$x = [\begin{array}{c} 8 & 1 \\ 3 - 5 & 0 + 2 \end{array}]$

Subtract $5$ from $3$ .

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

Add $0$ and $2$ .

$x = [\begin{array}{c} 8 & 1 \\ - 2 & 2 \end{array}]$