Solve the Matrix Equation [[-18,3,5]]-C=[[-22,1,12]]

$[\begin{array}{c} - 18 & 3 & 5 \end{array}] - C = [\begin{array}{c} - 22 & 1 & 12 \end{array}]$

Subtract the matrix from both sides of the equation.

$[\begin{array}{c} - 18 & 3 & 5 \end{array}] - X - [\begin{array}{c} - 18 & 3 & 5 \end{array}] = [\begin{array}{c} - 22 & 1 & 12 \end{array}] - [\begin{array}{c} - 18 & 3 & 5 \end{array}]$

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} - 18 - (- 18) & 3 - 3 & 5 - 5 \end{array}] - X = [\begin{array}{c} - 22 & 1 & 12 \end{array}] - [\begin{array}{c} - 18 & 3 & 5 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 18 - (- 18) & 3 - 3 & 5 - 5 \end{array}]$ .

Simplify $- 18 - (- 18)$ .

$[\begin{array}{c} 0 & 3 - 3 & 5 - 5 \end{array}] - X = [\begin{array}{c} - 22 & 1 & 12 \end{array}] - [\begin{array}{c} - 18 & 3 & 5 \end{array}]$

Simplify $3 - 3$ .

$[\begin{array}{c} 0 & 0 & 5 - 5 \end{array}] - X = [\begin{array}{c} - 22 & 1 & 12 \end{array}] - [\begin{array}{c} - 18 & 3 & 5 \end{array}]$

Simplify $5 - 5$ .

$[\begin{array}{c} 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 22 & 1 & 12 \end{array}] - [\begin{array}{c} - 18 & 3 & 5 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 22 - (- 18) & 1 - 3 & 12 - 5 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 22 - (- 18) & 1 - 3 & 12 - 5 \end{array}]$ .

Simplify $- 22 - (- 18)$ .

$[\begin{array}{c} 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 4 & 1 - 3 & 12 - 5 \end{array}]$

Simplify $1 - 3$ .

$[\begin{array}{c} 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 4 & - 2 & 12 - 5 \end{array}]$

Simplify $12 - 5$ .

$[\begin{array}{c} 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 4 & - 2 & 7 \end{array}]$

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

$- X = [\begin{array}{c} - 4 & - 2 & 7 \end{array}]$

Multiply both sides of the equation by $- 1$ .

$- 1 \cdot (- X) = - 1 \cdot [\begin{array}{c} - 4 & - 2 & 7 \end{array}]$

Simplify both sides of the equation.

Multiply $- 1 (- X)$ .

Multiply $- 1$ by $- 1$ .

$1 X = - 1 \cdot [\begin{array}{c} - 4 & - 2 & 7 \end{array}]$

Multiply $X$ by $1$ .

$X = - 1 \cdot [\begin{array}{c} - 4 & - 2 & 7 \end{array}]$

Simplify the right side of the equation.

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

$X = [\begin{array}{c} - 1 \cdot - 4 & - 1 \cdot - 2 & - 1 \cdot 7 \end{array}]$

Simplify each element in the matrix.

Rearrange $- 1 \cdot - 4$ .

$X = [\begin{array}{c} 4 & - 1 \cdot - 2 & - 1 \cdot 7 \end{array}]$

Rearrange $- 1 \cdot - 2$ .

$X = [\begin{array}{c} 4 & 2 & - 1 \cdot 7 \end{array}]$

Rearrange $- 1 \cdot 7$ .

$X = [\begin{array}{c} 4 & 2 & - 7 \end{array}]$

Solve the Matrix Equation [[-18,3,5]]-C=[[-22,1,12]]

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