Solve the Matrix Equation [[2,2,-7],[8,5,1],[3,12,-15]]-X=[[0,6,15],[-9,-18,19],[12,-7,3]]

$[\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}] - X = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}]$

Subtract the matrix from both sides of the equation.

$[\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}] - X - [\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}] = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}] - [\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}]$

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 2 - 2 & 2 - 2 & - 7 - (- 7) \\ 8 - 8 & 5 - 5 & 1 - 1 \\ 3 - 3 & 12 - 12 & - 15 - (- 15) \end{array}] - X = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}] - [\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 2 - 2 & 2 - 2 & - 7 - (- 7) \\ 8 - 8 & 5 - 5 & 1 - 1 \\ 3 - 3 & 12 - 12 & - 15 - (- 15) \end{array}]$ .

Simplify $2 - 2$ .

$[\begin{array}{c} 0 & 2 - 2 & - 7 - (- 7) \\ 8 - 8 & 5 - 5 & 1 - 1 \\ 3 - 3 & 12 - 12 & - 15 - (- 15) \end{array}] - X = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}] - [\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}]$

Simplify $2 - 2$ .

$[\begin{array}{c} 0 & 0 & - 7 - (- 7) \\ 8 - 8 & 5 - 5 & 1 - 1 \\ 3 - 3 & 12 - 12 & - 15 - (- 15) \end{array}] - X = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}] - [\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}]$

Simplify $- 7 - (- 7)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 8 - 8 & 5 - 5 & 1 - 1 \\ 3 - 3 & 12 - 12 & - 15 - (- 15) \end{array}] - X = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}] - [\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}]$

Simplify $8 - 8$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 5 - 5 & 1 - 1 \\ 3 - 3 & 12 - 12 & - 15 - (- 15) \end{array}] - X = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}] - [\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}]$

Simplify $5 - 5$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 1 - 1 \\ 3 - 3 & 12 - 12 & - 15 - (- 15) \end{array}] - X = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}] - [\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}]$

Simplify $1 - 1$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 3 - 3 & 12 - 12 & - 15 - (- 15) \end{array}] - X = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}] - [\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}]$

Simplify $3 - 3$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 12 - 12 & - 15 - (- 15) \end{array}] - X = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}] - [\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}]$

Simplify $12 - 12$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & - 15 - (- 15) \end{array}] - X = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}] - [\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}]$

Simplify $- 15 - (- 15)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} 0 & 6 & 15 \\ - 9 & - 18 & 19 \\ 12 & - 7 & 3 \end{array}] - [\begin{array}{c} 2 & 2 & - 7 \\ 8 & 5 & 1 \\ 3 & 12 & - 15 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} 0 - 2 & 6 - 2 & 15 - (- 7) \\ - 9 - 8 & - 18 - 5 & 19 - 1 \\ 12 - 3 & - 7 - 12 & 3 - (- 15) \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 0 - 2 & 6 - 2 & 15 - (- 7) \\ - 9 - 8 & - 18 - 5 & 19 - 1 \\ 12 - 3 & - 7 - 12 & 3 - (- 15) \end{array}]$ .

Simplify $0 - 2$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 2 & 6 - 2 & 15 - (- 7) \\ - 9 - 8 & - 18 - 5 & 19 - 1 \\ 12 - 3 & - 7 - 12 & 3 - (- 15) \end{array}]$

Simplify $6 - 2$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 2 & 4 & 15 - (- 7) \\ - 9 - 8 & - 18 - 5 & 19 - 1 \\ 12 - 3 & - 7 - 12 & 3 - (- 15) \end{array}]$

Simplify $15 - (- 7)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 2 & 4 & 22 \\ - 9 - 8 & - 18 - 5 & 19 - 1 \\ 12 - 3 & - 7 - 12 & 3 - (- 15) \end{array}]$

Simplify $- 9 - 8$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 18 - 5 & 19 - 1 \\ 12 - 3 & - 7 - 12 & 3 - (- 15) \end{array}]$

Simplify $- 18 - 5$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 19 - 1 \\ 12 - 3 & - 7 - 12 & 3 - (- 15) \end{array}]$

Simplify $19 - 1$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 12 - 3 & - 7 - 12 & 3 - (- 15) \end{array}]$

Simplify $12 - 3$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 9 & - 7 - 12 & 3 - (- 15) \end{array}]$

Simplify $- 7 - 12$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 9 & - 19 & 3 - (- 15) \end{array}]$

Simplify $3 - (- 15)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 9 & - 19 & 18 \end{array}]$

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

$- X = [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 9 & - 19 & 18 \end{array}]$

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

$- 1 \cdot (- X) = - 1 \cdot [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 9 & - 19 & 18 \end{array}]$

Simplify both sides of the equation.

Multiply $- 1 (- X)$ .

Multiply $- 1$ by $- 1$ .

$1 X = - 1 \cdot [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 9 & - 19 & 18 \end{array}]$

Multiply $X$ by $1$ .

$X = - 1 \cdot [\begin{array}{c} - 2 & 4 & 22 \\ - 17 & - 23 & 18 \\ 9 & - 19 & 18 \end{array}]$

Simplify the right side of the equation.

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

$X = [\begin{array}{c} - 1 \cdot - 2 & - 1 \cdot 4 & - 1 \cdot 22 \\ - 1 \cdot - 17 & - 1 \cdot - 23 & - 1 \cdot 18 \\ - 1 \cdot 9 & - 1 \cdot - 19 & - 1 \cdot 18 \end{array}]$

Simplify each element in the matrix.

Rearrange $- 1 \cdot - 2$ .

$X = [\begin{array}{c} 2 & - 1 \cdot 4 & - 1 \cdot 22 \\ - 1 \cdot - 17 & - 1 \cdot - 23 & - 1 \cdot 18 \\ - 1 \cdot 9 & - 1 \cdot - 19 & - 1 \cdot 18 \end{array}]$

Rearrange $- 1 \cdot 4$ .

$X = [\begin{array}{c} 2 & - 4 & - 1 \cdot 22 \\ - 1 \cdot - 17 & - 1 \cdot - 23 & - 1 \cdot 18 \\ - 1 \cdot 9 & - 1 \cdot - 19 & - 1 \cdot 18 \end{array}]$

Rearrange $- 1 \cdot 22$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ - 1 \cdot - 17 & - 1 \cdot - 23 & - 1 \cdot 18 \\ - 1 \cdot 9 & - 1 \cdot - 19 & - 1 \cdot 18 \end{array}]$

Rearrange $- 1 \cdot - 17$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ 17 & - 1 \cdot - 23 & - 1 \cdot 18 \\ - 1 \cdot 9 & - 1 \cdot - 19 & - 1 \cdot 18 \end{array}]$

Rearrange $- 1 \cdot - 23$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ 17 & 23 & - 1 \cdot 18 \\ - 1 \cdot 9 & - 1 \cdot - 19 & - 1 \cdot 18 \end{array}]$

Rearrange $- 1 \cdot 18$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ 17 & 23 & - 18 \\ - 1 \cdot 9 & - 1 \cdot - 19 & - 1 \cdot 18 \end{array}]$

Rearrange $- 1 \cdot 9$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ 17 & 23 & - 18 \\ - 9 & - 1 \cdot - 19 & - 1 \cdot 18 \end{array}]$

Rearrange $- 1 \cdot - 19$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ 17 & 23 & - 18 \\ - 9 & 19 & - 1 \cdot 18 \end{array}]$

Rearrange $- 1 \cdot 18$ .

$X = [\begin{array}{c} 2 & - 4 & - 22 \\ 17 & 23 & - 18 \\ - 9 & 19 & - 18 \end{array}]$

Solve the Matrix Equation [[2,2,-7],[8,5,1],[3,12,-15]]-X=[[0,6,15],[-9,-18,19],[12,-7,3]]

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