Solve the Matrix Equation x-[[2,-3,8],[-4,3,0]]=[[6,-1,-5],[-5,2,-4]]

$x - [\begin{array}{c} 2 & - 3 & 8 \\ - 4 & 3 & 0 \end{array}] = [\begin{array}{c} 6 & - 1 & - 5 \\ - 5 & 2 & - 4 \end{array}]$

Step 1

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

Add $[\begin{array}{c} 2 & - 3 & 8 \\ - 4 & 3 & 0 \end{array}]$ to both sides of the equation.

$x = [\begin{array}{c} 6 & - 1 & - 5 \\ - 5 & 2 & - 4 \end{array}] + [\begin{array}{c} 2 & - 3 & 8 \\ - 4 & 3 & 0 \end{array}]$

Step 2

Simplify the right side.

Add the corresponding elements.

$x = [\begin{array}{c} 6 + 2 & - 1 - 3 & - 5 + 8 \\ - 5 - 4 & 2 + 3 & - 4 + 0 \end{array}]$

Simplify each element.

Add $6$ and $2$ .

$x = [\begin{array}{c} 8 & - 1 - 3 & - 5 + 8 \\ - 5 - 4 & 2 + 3 & - 4 + 0 \end{array}]$

Subtract $3$ from $- 1$ .

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

Add $- 5$ and $8$ .

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

Subtract $4$ from $- 5$ .

$x = [\begin{array}{c} 8 & - 4 & 3 \\ - 9 & 2 + 3 & - 4 + 0 \end{array}]$

Add $2$ and $3$ .

$x = [\begin{array}{c} 8 & - 4 & 3 \\ - 9 & 5 & - 4 + 0 \end{array}]$

Add $- 4$ and $0$ .

$x = [\begin{array}{c} 8 & - 4 & 3 \\ - 9 & 5 & - 4 \end{array}]$