Solve the Matrix Equation x+[[-10,3,-14],[21,8,-5],[2,6,-1]]=[[10,2,3],[4,-10,2],[3,4,-1]]

$x + [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}] = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}]$

Subtract the matrix from both sides of the equation.

$X + [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}] - [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}] = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}] - [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}]$

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} - 10 - (- 10) & 3 - 3 & - 14 - (- 14) \\ 21 - 21 & 8 - 8 & - 5 - (- 5) \\ 2 - 2 & 6 - 6 & - 1 - (- 1) \end{array}] + X = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}] - [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 10 - (- 10) & 3 - 3 & - 14 - (- 14) \\ 21 - 21 & 8 - 8 & - 5 - (- 5) \\ 2 - 2 & 6 - 6 & - 1 - (- 1) \end{array}]$ .

Simplify $- 10 - (- 10)$ .

$[\begin{array}{c} 0 & 3 - 3 & - 14 - (- 14) \\ 21 - 21 & 8 - 8 & - 5 - (- 5) \\ 2 - 2 & 6 - 6 & - 1 - (- 1) \end{array}] + X = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}] - [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}]$

Simplify $3 - 3$ .

$[\begin{array}{c} 0 & 0 & - 14 - (- 14) \\ 21 - 21 & 8 - 8 & - 5 - (- 5) \\ 2 - 2 & 6 - 6 & - 1 - (- 1) \end{array}] + X = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}] - [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}]$

Simplify $- 14 - (- 14)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 21 - 21 & 8 - 8 & - 5 - (- 5) \\ 2 - 2 & 6 - 6 & - 1 - (- 1) \end{array}] + X = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}] - [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}]$

Simplify $21 - 21$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 8 - 8 & - 5 - (- 5) \\ 2 - 2 & 6 - 6 & - 1 - (- 1) \end{array}] + X = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}] - [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}]$

Simplify $8 - 8$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & - 5 - (- 5) \\ 2 - 2 & 6 - 6 & - 1 - (- 1) \end{array}] + X = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}] - [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}]$

Simplify $- 5 - (- 5)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 2 - 2 & 6 - 6 & - 1 - (- 1) \end{array}] + X = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}] - [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}]$

Simplify $2 - 2$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 6 - 6 & - 1 - (- 1) \end{array}] + X = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}] - [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}]$

Simplify $6 - 6$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & - 1 - (- 1) \end{array}] + X = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}] - [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}]$

Simplify $- 1 - (- 1)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 10 & 2 & 3 \\ 4 & - 10 & 2 \\ 3 & 4 & - 1 \end{array}] - [\begin{array}{c} - 10 & 3 & - 14 \\ 21 & 8 & - 5 \\ 2 & 6 & - 1 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 10 - (- 10) & 2 - 3 & 3 - (- 14) \\ 4 - 21 & - 10 - 8 & 2 - (- 5) \\ 3 - 2 & 4 - 6 & - 1 - (- 1) \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 10 - (- 10) & 2 - 3 & 3 - (- 14) \\ 4 - 21 & - 10 - 8 & 2 - (- 5) \\ 3 - 2 & 4 - 6 & - 1 - (- 1) \end{array}]$ .

Simplify $10 - (- 10)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 20 & 2 - 3 & 3 - (- 14) \\ 4 - 21 & - 10 - 8 & 2 - (- 5) \\ 3 - 2 & 4 - 6 & - 1 - (- 1) \end{array}]$

Simplify $2 - 3$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 20 & - 1 & 3 - (- 14) \\ 4 - 21 & - 10 - 8 & 2 - (- 5) \\ 3 - 2 & 4 - 6 & - 1 - (- 1) \end{array}]$

Simplify $3 - (- 14)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 20 & - 1 & 17 \\ 4 - 21 & - 10 - 8 & 2 - (- 5) \\ 3 - 2 & 4 - 6 & - 1 - (- 1) \end{array}]$

Simplify $4 - 21$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 10 - 8 & 2 - (- 5) \\ 3 - 2 & 4 - 6 & - 1 - (- 1) \end{array}]$

Simplify $- 10 - 8$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 18 & 2 - (- 5) \\ 3 - 2 & 4 - 6 & - 1 - (- 1) \end{array}]$

Simplify $2 - (- 5)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 18 & 7 \\ 3 - 2 & 4 - 6 & - 1 - (- 1) \end{array}]$

Simplify $3 - 2$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 18 & 7 \\ 1 & 4 - 6 & - 1 - (- 1) \end{array}]$

Simplify $4 - 6$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 18 & 7 \\ 1 & - 2 & - 1 - (- 1) \end{array}]$

Simplify $- 1 - (- 1)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 18 & 7 \\ 1 & - 2 & 0 \end{array}]$

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

$X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 18 & 7 \\ 1 & - 2 & 0 \end{array}]$

The matrix is in the most simplified form.

$X = [\begin{array}{c} 20 & - 1 & 17 \\ - 17 & - 18 & 7 \\ 1 & - 2 & 0 \end{array}]$

Solve the Matrix Equation x+[[-10,3,-14],[21,8,-5],[2,6,-1]]=[[10,2,3],[4,-10,2],[3,4,-1]]

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