Solve the Matrix Equation -8[[2,11,4],[0,2,-6]]=[[-16,-88,x],[0,-16,48]]

$- 8 [\begin{array}{c} 2 & 11 & 4 \\ 0 & 2 & - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Step 1

Simplify the left side of the equation.

Multiply $- 8$ by each element of the matrix.

$[\begin{array}{c} - 8 \cdot 2 & - 8 \cdot 11 & - 8 \cdot 4 \\ - 8 \cdot 0 & - 8 \cdot 2 & - 8 \cdot - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Simplify each element in the matrix.

Rearrange $- 8 \cdot 2$ .

$[\begin{array}{c} - 16 & - 8 \cdot 11 & - 8 \cdot 4 \\ - 8 \cdot 0 & - 8 \cdot 2 & - 8 \cdot - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Rearrange $- 8 \cdot 11$ .

$[\begin{array}{c} - 16 & - 88 & - 8 \cdot 4 \\ - 8 \cdot 0 & - 8 \cdot 2 & - 8 \cdot - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Rearrange $- 8 \cdot 4$ .

$[\begin{array}{c} - 16 & - 88 & - 32 \\ - 8 \cdot 0 & - 8 \cdot 2 & - 8 \cdot - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Rearrange $- 8 \cdot 0$ .

$[\begin{array}{c} - 16 & - 88 & - 32 \\ 0 & - 8 \cdot 2 & - 8 \cdot - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Rearrange $- 8 \cdot 2$ .

$[\begin{array}{c} - 16 & - 88 & - 32 \\ 0 & - 16 & - 8 \cdot - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Rearrange $- 8 \cdot - 6$ .

$[\begin{array}{c} - 16 & - 88 & - 32 \\ 0 & - 16 & 48 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Step 2

The matrix equation can be written as a set of equations.

$- 16 = - 16$

$- 88 = - 88$

$- 32 = x$

$0 = 0$

$- 16 = - 16$

$48 = 48$

Step 3

Rewrite the equation as $x = - 32$ .

$x = - 32$

Solve the Matrix Equation -8[[2,11,4],[0,2,-6]]=[[-16,-88,x],[0,-16,48]]

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