Solve the Matrix Equation X+[[20,-9,-3],[19,-2,-5],[-1,0,-8]]=[[-7,92,-5],[0,91,-6],[-9,-1,12]]

$X + [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}] = [\begin{array}{c} - 7 & 92 & - 5 \\ 0 & 91 & - 6 \\ - 9 & - 1 & 12 \end{array}]$

Subtract the matrix from both sides of the equation.

$X + [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}] - [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}] = [\begin{array}{c} - 7 & 92 & - 5 \\ 0 & 91 & - 6 \\ - 9 & - 1 & 12 \end{array}] - [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}]$

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 20 - 20 & - 9 - (- 9) & - 3 - (- 3) \\ 19 - 19 & - 2 - (- 2) & - 5 - (- 5) \\ - 1 - (- 1) & 0 - 0 & - 8 - (- 8) \end{array}] + X = [\begin{array}{c} - 7 & 92 & - 5 \\ 0 & 91 & - 6 \\ - 9 & - 1 & 12 \end{array}] - [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 20 - 20 & - 9 - (- 9) & - 3 - (- 3) \\ 19 - 19 & - 2 - (- 2) & - 5 - (- 5) \\ - 1 - (- 1) & 0 - 0 & - 8 - (- 8) \end{array}]$ .

Simplify $20 - 20$ .

$[\begin{array}{c} 0 & - 9 - (- 9) & - 3 - (- 3) \\ 19 - 19 & - 2 - (- 2) & - 5 - (- 5) \\ - 1 - (- 1) & 0 - 0 & - 8 - (- 8) \end{array}] + X = [\begin{array}{c} - 7 & 92 & - 5 \\ 0 & 91 & - 6 \\ - 9 & - 1 & 12 \end{array}] - [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}]$

Simplify $- 9 - (- 9)$ .

$[\begin{array}{c} 0 & 0 & - 3 - (- 3) \\ 19 - 19 & - 2 - (- 2) & - 5 - (- 5) \\ - 1 - (- 1) & 0 - 0 & - 8 - (- 8) \end{array}] + X = [\begin{array}{c} - 7 & 92 & - 5 \\ 0 & 91 & - 6 \\ - 9 & - 1 & 12 \end{array}] - [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}]$

Simplify $- 3 - (- 3)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 19 - 19 & - 2 - (- 2) & - 5 - (- 5) \\ - 1 - (- 1) & 0 - 0 & - 8 - (- 8) \end{array}] + X = [\begin{array}{c} - 7 & 92 & - 5 \\ 0 & 91 & - 6 \\ - 9 & - 1 & 12 \end{array}] - [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}]$

Simplify $19 - 19$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & - 2 - (- 2) & - 5 - (- 5) \\ - 1 - (- 1) & 0 - 0 & - 8 - (- 8) \end{array}] + X = [\begin{array}{c} - 7 & 92 & - 5 \\ 0 & 91 & - 6 \\ - 9 & - 1 & 12 \end{array}] - [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}]$

Simplify $- 2 - (- 2)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & - 5 - (- 5) \\ - 1 - (- 1) & 0 - 0 & - 8 - (- 8) \end{array}] + X = [\begin{array}{c} - 7 & 92 & - 5 \\ 0 & 91 & - 6 \\ - 9 & - 1 & 12 \end{array}] - [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}]$

Simplify $- 5 - (- 5)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ - 1 - (- 1) & 0 - 0 & - 8 - (- 8) \end{array}] + X = [\begin{array}{c} - 7 & 92 & - 5 \\ 0 & 91 & - 6 \\ - 9 & - 1 & 12 \end{array}] - [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}]$

Simplify $- 1 - (- 1)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 - 0 & - 8 - (- 8) \end{array}] + X = [\begin{array}{c} - 7 & 92 & - 5 \\ 0 & 91 & - 6 \\ - 9 & - 1 & 12 \end{array}] - [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}]$

Simplify $0 - 0$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & - 8 - (- 8) \end{array}] + X = [\begin{array}{c} - 7 & 92 & - 5 \\ 0 & 91 & - 6 \\ - 9 & - 1 & 12 \end{array}] - [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}]$

Simplify $- 8 - (- 8)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 7 & 92 & - 5 \\ 0 & 91 & - 6 \\ - 9 & - 1 & 12 \end{array}] - [\begin{array}{c} 20 & - 9 & - 3 \\ 19 & - 2 & - 5 \\ - 1 & 0 & - 8 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 7 - 20 & 92 - (- 9) & - 5 - (- 3) \\ 0 - 19 & 91 - (- 2) & - 6 - (- 5) \\ - 9 - (- 1) & - 1 - 0 & 12 - (- 8) \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 7 - 20 & 92 - (- 9) & - 5 - (- 3) \\ 0 - 19 & 91 - (- 2) & - 6 - (- 5) \\ - 9 - (- 1) & - 1 - 0 & 12 - (- 8) \end{array}]$ .

Simplify $- 7 - 20$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 27 & 92 - (- 9) & - 5 - (- 3) \\ 0 - 19 & 91 - (- 2) & - 6 - (- 5) \\ - 9 - (- 1) & - 1 - 0 & 12 - (- 8) \end{array}]$

Simplify $92 - (- 9)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 27 & 101 & - 5 - (- 3) \\ 0 - 19 & 91 - (- 2) & - 6 - (- 5) \\ - 9 - (- 1) & - 1 - 0 & 12 - (- 8) \end{array}]$

Simplify $- 5 - (- 3)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 27 & 101 & - 2 \\ 0 - 19 & 91 - (- 2) & - 6 - (- 5) \\ - 9 - (- 1) & - 1 - 0 & 12 - (- 8) \end{array}]$

Simplify $0 - 19$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 27 & 101 & - 2 \\ - 19 & 91 - (- 2) & - 6 - (- 5) \\ - 9 - (- 1) & - 1 - 0 & 12 - (- 8) \end{array}]$

Simplify $91 - (- 2)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 27 & 101 & - 2 \\ - 19 & 93 & - 6 - (- 5) \\ - 9 - (- 1) & - 1 - 0 & 12 - (- 8) \end{array}]$

Simplify $- 6 - (- 5)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 27 & 101 & - 2 \\ - 19 & 93 & - 1 \\ - 9 - (- 1) & - 1 - 0 & 12 - (- 8) \end{array}]$

Simplify $- 9 - (- 1)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 27 & 101 & - 2 \\ - 19 & 93 & - 1 \\ - 8 & - 1 - 0 & 12 - (- 8) \end{array}]$

Simplify $- 1 - 0$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 27 & 101 & - 2 \\ - 19 & 93 & - 1 \\ - 8 & - 1 & 12 - (- 8) \end{array}]$

Simplify $12 - (- 8)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 27 & 101 & - 2 \\ - 19 & 93 & - 1 \\ - 8 & - 1 & 20 \end{array}]$

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

$X = [\begin{array}{c} - 27 & 101 & - 2 \\ - 19 & 93 & - 1 \\ - 8 & - 1 & 20 \end{array}]$

The matrix is in the most simplified form.

$X = [\begin{array}{c} - 27 & 101 & - 2 \\ - 19 & 93 & - 1 \\ - 8 & - 1 & 20 \end{array}]$

Solve the Matrix Equation X+[[20,-9,-3],[19,-2,-5],[-1,0,-8]]=[[-7,92,-5],[0,91,-6],[-9,-1,12]]

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