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

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

Multiply $- 5$ by each element of the matrix.

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

Simplify each element in the matrix.

Rearrange $- 5 \cdot 2$ .

$- 2 x + [\begin{array}{c} - 10 & - 5 \cdot - 8 \\ - 5 \cdot - 4 & - 5 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Rearrange $- 5 \cdot - 8$ .

$- 2 x + [\begin{array}{c} - 10 & 40 \\ - 5 \cdot - 4 & - 5 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Rearrange $- 5 \cdot - 4$ .

$- 2 x + [\begin{array}{c} - 10 & 40 \\ 20 & - 5 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Rearrange $- 5 \cdot 2$ .

$- 2 x + [\begin{array}{c} - 10 & 40 \\ 20 & - 10 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Subtract the matrix from both sides of the equation.

$- 2 X + [\begin{array}{c} - 10 & 40 \\ 20 & - 10 \end{array}] - [\begin{array}{c} - 10 & 40 \\ 20 & - 10 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}] - [\begin{array}{c} - 10 & 40 \\ 20 & - 10 \end{array}]$

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} - 10 - (- 10) & 40 - 40 \\ 20 - 20 & - 10 - (- 10) \end{array}] - 2 X = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}] - [\begin{array}{c} - 10 & 40 \\ 20 & - 10 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 10 - (- 10) & 40 - 40 \\ 20 - 20 & - 10 - (- 10) \end{array}]$ .

Simplify $- 10 - (- 10)$ .

$[\begin{array}{c} 0 & 40 - 40 \\ 20 - 20 & - 10 - (- 10) \end{array}] - 2 X = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}] - [\begin{array}{c} - 10 & 40 \\ 20 & - 10 \end{array}]$

Simplify $40 - 40$ .

$[\begin{array}{c} 0 & 0 \\ 20 - 20 & - 10 - (- 10) \end{array}] - 2 X = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}] - [\begin{array}{c} - 10 & 40 \\ 20 & - 10 \end{array}]$

Simplify $20 - 20$ .

$[\begin{array}{c} 0 & 0 \\ 0 & - 10 - (- 10) \end{array}] - 2 X = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}] - [\begin{array}{c} - 10 & 40 \\ 20 & - 10 \end{array}]$

Simplify $- 10 - (- 10)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] - 2 X = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}] - [\begin{array}{c} - 10 & 40 \\ 20 & - 10 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] - 2 X = [\begin{array}{c} 4 - (- 10) & - 6 - 40 \\ 2 - 20 & - 8 - (- 10) \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 4 - (- 10) & - 6 - 40 \\ 2 - 20 & - 8 - (- 10) \end{array}]$ .

Simplify $4 - (- 10)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] - 2 X = [\begin{array}{c} 14 & - 6 - 40 \\ 2 - 20 & - 8 - (- 10) \end{array}]$

Simplify $- 6 - 40$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] - 2 X = [\begin{array}{c} 14 & - 46 \\ 2 - 20 & - 8 - (- 10) \end{array}]$

Simplify $2 - 20$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] - 2 X = [\begin{array}{c} 14 & - 46 \\ - 18 & - 8 - (- 10) \end{array}]$

Simplify $- 8 - (- 10)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] - 2 X = [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Adding the null matrix to any matrix is a matrix itself.

$- 2 X = [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Multiply both sides of the equation by $- \frac{1}{2}$ .

$- \frac{1}{2} \cdot (- 2 X) = - \frac{1}{2} \cdot [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Simplify both sides of the equation.

Simplify the left side of the equation.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} \cdot (- 2 X) = - \frac{1}{2} \cdot [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Factor $2$ out of $- 2 X$ .

$\frac{- 1}{2} \cdot (2 (- X)) = - \frac{1}{2} \cdot [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Cancel the common factor.

$\frac{- 1}{2} \cdot (2 (- X)) = - \frac{1}{2} \cdot [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Rewrite the expression.

$- 1 \cdot (- X) = - \frac{1}{2} \cdot [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 \cdot X = - \frac{1}{2} \cdot [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Multiply $X$ by $1$ .

$X = - \frac{1}{2} \cdot [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Simplify the right side of the equation.

Multiply $- \frac{1}{2}$ by each element of the matrix.

$X = [\begin{array}{c} - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot - 46 \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Simplify each element in the matrix.

Rearrange $- \frac{1}{2} \cdot 14$ .

$X = [\begin{array}{c} - 7 & - \frac{1}{2} \cdot - 46 \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Rearrange $- \frac{1}{2} \cdot - 46$ .

$X = [\begin{array}{c} - 7 & 23 \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Rearrange $- \frac{1}{2} \cdot - 18$ .

$X = [\begin{array}{c} - 7 & 23 \\ 9 & - \frac{1}{2} \cdot 2 \end{array}]$

Rearrange $- \frac{1}{2} \cdot 2$ .

$X = [\begin{array}{c} - 7 & 23 \\ 9 & - 1 \end{array}]$

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

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