Solve the Matrix Equation -x+3[[2,-8],[-4,2]]=[[4,-6],[2,-8]]

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

Step 1

Simplify each term.

Multiply $3$ by each element of the matrix.

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

Simplify each element in the matrix.

Multiply $3$ by $2$ .

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

Multiply $3$ by $- 8$ .

$- x + [\begin{array}{c} 6 & - 24 \\ 3 \cdot - 4 & 3 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Multiply $3$ by $- 4$ .

$- x + [\begin{array}{c} 6 & - 24 \\ - 12 & 3 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Multiply $3$ by $2$ .

$- x + [\begin{array}{c} 6 & - 24 \\ - 12 & 6 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 2

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

Subtract $[\begin{array}{c} 6 & - 24 \\ - 12 & 6 \end{array}]$ from both sides of the equation.

$- x = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}] - [\begin{array}{c} 6 & - 24 \\ - 12 & 6 \end{array}]$

Step 3

Simplify the right side.

Subtract the corresponding elements.

$- x = [\begin{array}{c} 4 - 6 & - 6 + 24 \\ 2 + 12 & - 8 - 6 \end{array}]$

Simplify each element.

Subtract $6$ from $4$ .

$- x = [\begin{array}{c} - 2 & - 6 + 24 \\ 2 + 12 & - 8 - 6 \end{array}]$

Add $- 6$ and $24$ .

$- x = [\begin{array}{c} - 2 & 18 \\ 2 + 12 & - 8 - 6 \end{array}]$

Add $2$ and $12$ .

$- x = [\begin{array}{c} - 2 & 18 \\ 14 & - 8 - 6 \end{array}]$

Subtract $6$ from $- 8$ .

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

Step 4

Multiply both sides by $- 1$ .

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

Step 5

Simplify.

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$1 x = - [\begin{array}{c} - 2 & 18 \\ 14 & - 14 \end{array}]$

Multiply $x$ by $1$ .

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

Multiply $- 1$ by each element of the matrix.

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

Simplify each element in the matrix.

Multiply $- 1$ by $- 2$ .

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

Multiply $- 1$ by $18$ .

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

Multiply $- 1$ by $14$ .

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

Multiply $- 1$ by $- 14$ .

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

Solve the Matrix Equation -x+3[[2,-8],[-4,2]]=[[4,-6],[2,-8]]

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