Solve the Matrix Equation x-2[[2,-8],[-4,2]]=[[4,-6],[2,-8]]

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

Step 1

Simplify each term.

Multiply $- 2$ by each element of the matrix.

$x + [\begin{array}{c} - 2 \cdot 2 & - 2 \cdot - 8 \\ - 2 \cdot - 4 & - 2 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Simplify each element in the matrix.

Multiply $- 2$ by $2$ .

$x + [\begin{array}{c} - 4 & - 2 \cdot - 8 \\ - 2 \cdot - 4 & - 2 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Multiply $- 2$ by $- 8$ .

$x + [\begin{array}{c} - 4 & 16 \\ - 2 \cdot - 4 & - 2 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Multiply $- 2$ by $- 4$ .

$x + [\begin{array}{c} - 4 & 16 \\ 8 & - 2 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Multiply $- 2$ by $2$ .

$x + [\begin{array}{c} - 4 & 16 \\ 8 & - 4 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 2

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

Subtract $[\begin{array}{c} - 4 & 16 \\ 8 & - 4 \end{array}]$ from both sides of the equation.

$x = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}] - [\begin{array}{c} - 4 & 16 \\ 8 & - 4 \end{array}]$

Step 3

Simplify the right side.

Subtract the corresponding elements.

$x = [\begin{array}{c} 4 + 4 & - 6 - 16 \\ 2 - 8 & - 8 + 4 \end{array}]$

Simplify each element.

Add $4$ and $4$ .

$x = [\begin{array}{c} 8 & - 6 - 16 \\ 2 - 8 & - 8 + 4 \end{array}]$

Subtract $16$ from $- 6$ .

$x = [\begin{array}{c} 8 & - 22 \\ 2 - 8 & - 8 + 4 \end{array}]$

Subtract $8$ from $2$ .

$x = [\begin{array}{c} 8 & - 22 \\ - 6 & - 8 + 4 \end{array}]$

Add $- 8$ and $4$ .

$x = [\begin{array}{c} 8 & - 22 \\ - 6 & - 4 \end{array}]$