Solve the Matrix Equation D+[[1,0,1],[-3,9,-7],[-20,2,4]]=[[9,-3,2],[8,-1,0],[11,15,3]]

$D + [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}] = [\begin{array}{c} 9 & - 3 & 2 \\ 8 & - 1 & 0 \\ 11 & 15 & 3 \end{array}]$

Subtract the matrix from both sides of the equation.

$X + [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}] - [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}] = [\begin{array}{c} 9 & - 3 & 2 \\ 8 & - 1 & 0 \\ 11 & 15 & 3 \end{array}] - [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}]$

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 1 - 1 & 0 - 0 & 1 - 1 \\ - 3 - (- 3) & 9 - 9 & - 7 - (- 7) \\ - 20 - (- 20) & 2 - 2 & 4 - 4 \end{array}] + X = [\begin{array}{c} 9 & - 3 & 2 \\ 8 & - 1 & 0 \\ 11 & 15 & 3 \end{array}] - [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 1 - 1 & 0 - 0 & 1 - 1 \\ - 3 - (- 3) & 9 - 9 & - 7 - (- 7) \\ - 20 - (- 20) & 2 - 2 & 4 - 4 \end{array}]$ .

Simplify $1 - 1$ .

$[\begin{array}{c} 0 & 0 - 0 & 1 - 1 \\ - 3 - (- 3) & 9 - 9 & - 7 - (- 7) \\ - 20 - (- 20) & 2 - 2 & 4 - 4 \end{array}] + X = [\begin{array}{c} 9 & - 3 & 2 \\ 8 & - 1 & 0 \\ 11 & 15 & 3 \end{array}] - [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}]$

Simplify $0 - 0$ .

$[\begin{array}{c} 0 & 0 & 1 - 1 \\ - 3 - (- 3) & 9 - 9 & - 7 - (- 7) \\ - 20 - (- 20) & 2 - 2 & 4 - 4 \end{array}] + X = [\begin{array}{c} 9 & - 3 & 2 \\ 8 & - 1 & 0 \\ 11 & 15 & 3 \end{array}] - [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}]$

Simplify $1 - 1$ .

$[\begin{array}{c} 0 & 0 & 0 \\ - 3 - (- 3) & 9 - 9 & - 7 - (- 7) \\ - 20 - (- 20) & 2 - 2 & 4 - 4 \end{array}] + X = [\begin{array}{c} 9 & - 3 & 2 \\ 8 & - 1 & 0 \\ 11 & 15 & 3 \end{array}] - [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}]$

Simplify $- 3 - (- 3)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 9 - 9 & - 7 - (- 7) \\ - 20 - (- 20) & 2 - 2 & 4 - 4 \end{array}] + X = [\begin{array}{c} 9 & - 3 & 2 \\ 8 & - 1 & 0 \\ 11 & 15 & 3 \end{array}] - [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}]$

Simplify $9 - 9$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & - 7 - (- 7) \\ - 20 - (- 20) & 2 - 2 & 4 - 4 \end{array}] + X = [\begin{array}{c} 9 & - 3 & 2 \\ 8 & - 1 & 0 \\ 11 & 15 & 3 \end{array}] - [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}]$

Simplify $- 7 - (- 7)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ - 20 - (- 20) & 2 - 2 & 4 - 4 \end{array}] + X = [\begin{array}{c} 9 & - 3 & 2 \\ 8 & - 1 & 0 \\ 11 & 15 & 3 \end{array}] - [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}]$

Simplify $- 20 - (- 20)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 2 - 2 & 4 - 4 \end{array}] + X = [\begin{array}{c} 9 & - 3 & 2 \\ 8 & - 1 & 0 \\ 11 & 15 & 3 \end{array}] - [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}]$

Simplify $2 - 2$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 4 - 4 \end{array}] + X = [\begin{array}{c} 9 & - 3 & 2 \\ 8 & - 1 & 0 \\ 11 & 15 & 3 \end{array}] - [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}]$

Simplify $4 - 4$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 9 & - 3 & 2 \\ 8 & - 1 & 0 \\ 11 & 15 & 3 \end{array}] - [\begin{array}{c} 1 & 0 & 1 \\ - 3 & 9 & - 7 \\ - 20 & 2 & 4 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 9 - 1 & - 3 - 0 & 2 - 1 \\ 8 - (- 3) & - 1 - 9 & 0 - (- 7) \\ 11 - (- 20) & 15 - 2 & 3 - 4 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 9 - 1 & - 3 - 0 & 2 - 1 \\ 8 - (- 3) & - 1 - 9 & 0 - (- 7) \\ 11 - (- 20) & 15 - 2 & 3 - 4 \end{array}]$ .

Simplify $9 - 1$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & - 3 - 0 & 2 - 1 \\ 8 - (- 3) & - 1 - 9 & 0 - (- 7) \\ 11 - (- 20) & 15 - 2 & 3 - 4 \end{array}]$

Simplify $- 3 - 0$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & - 3 & 2 - 1 \\ 8 - (- 3) & - 1 - 9 & 0 - (- 7) \\ 11 - (- 20) & 15 - 2 & 3 - 4 \end{array}]$

Simplify $2 - 1$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & - 3 & 1 \\ 8 - (- 3) & - 1 - 9 & 0 - (- 7) \\ 11 - (- 20) & 15 - 2 & 3 - 4 \end{array}]$

Simplify $8 - (- 3)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & - 3 & 1 \\ 11 & - 1 - 9 & 0 - (- 7) \\ 11 - (- 20) & 15 - 2 & 3 - 4 \end{array}]$

Simplify $- 1 - 9$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & - 3 & 1 \\ 11 & - 10 & 0 - (- 7) \\ 11 - (- 20) & 15 - 2 & 3 - 4 \end{array}]$

Simplify $0 - (- 7)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & - 3 & 1 \\ 11 & - 10 & 7 \\ 11 - (- 20) & 15 - 2 & 3 - 4 \end{array}]$

Simplify $11 - (- 20)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & - 3 & 1 \\ 11 & - 10 & 7 \\ 31 & 15 - 2 & 3 - 4 \end{array}]$

Simplify $15 - 2$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & - 3 & 1 \\ 11 & - 10 & 7 \\ 31 & 13 & 3 - 4 \end{array}]$

Simplify $3 - 4$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & - 3 & 1 \\ 11 & - 10 & 7 \\ 31 & 13 & - 1 \end{array}]$

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

$X = [\begin{array}{c} 8 & - 3 & 1 \\ 11 & - 10 & 7 \\ 31 & 13 & - 1 \end{array}]$

The matrix is in the most simplified form.

$X = [\begin{array}{c} 8 & - 3 & 1 \\ 11 & - 10 & 7 \\ 31 & 13 & - 1 \end{array}]$

Solve the Matrix Equation D+[[1,0,1],[-3,9,-7],[-20,2,4]]=[[9,-3,2],[8,-1,0],[11,15,3]]

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