Solve the Matrix Equation x+[[12,14],[19,21],[3,-14]]=[[-2,-5],[13,7],[-9,12]]

$x + [\begin{array}{c} 12 & 14 \\ 19 & 21 \\ 3 & - 14 \end{array}] = [\begin{array}{c} - 2 & - 5 \\ 13 & 7 \\ - 9 & 12 \end{array}]$

Subtract the matrix from both sides of the equation.

$X + [\begin{array}{c} 12 & 14 \\ 19 & 21 \\ 3 & - 14 \end{array}] - [\begin{array}{c} 12 & 14 \\ 19 & 21 \\ 3 & - 14 \end{array}] = [\begin{array}{c} - 2 & - 5 \\ 13 & 7 \\ - 9 & 12 \end{array}] - [\begin{array}{c} 12 & 14 \\ 19 & 21 \\ 3 & - 14 \end{array}]$

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 12 - 12 & 14 - 14 \\ 19 - 19 & 21 - 21 \\ 3 - 3 & - 14 - (- 14) \end{array}] + X = [\begin{array}{c} - 2 & - 5 \\ 13 & 7 \\ - 9 & 12 \end{array}] - [\begin{array}{c} 12 & 14 \\ 19 & 21 \\ 3 & - 14 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 12 - 12 & 14 - 14 \\ 19 - 19 & 21 - 21 \\ 3 - 3 & - 14 - (- 14) \end{array}]$ .

Simplify $12 - 12$ .

$[\begin{array}{c} 0 & 14 - 14 \\ 19 - 19 & 21 - 21 \\ 3 - 3 & - 14 - (- 14) \end{array}] + X = [\begin{array}{c} - 2 & - 5 \\ 13 & 7 \\ - 9 & 12 \end{array}] - [\begin{array}{c} 12 & 14 \\ 19 & 21 \\ 3 & - 14 \end{array}]$

Simplify $14 - 14$ .

$[\begin{array}{c} 0 & 0 \\ 19 - 19 & 21 - 21 \\ 3 - 3 & - 14 - (- 14) \end{array}] + X = [\begin{array}{c} - 2 & - 5 \\ 13 & 7 \\ - 9 & 12 \end{array}] - [\begin{array}{c} 12 & 14 \\ 19 & 21 \\ 3 & - 14 \end{array}]$

Simplify $19 - 19$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 21 - 21 \\ 3 - 3 & - 14 - (- 14) \end{array}] + X = [\begin{array}{c} - 2 & - 5 \\ 13 & 7 \\ - 9 & 12 \end{array}] - [\begin{array}{c} 12 & 14 \\ 19 & 21 \\ 3 & - 14 \end{array}]$

Simplify $21 - 21$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 3 - 3 & - 14 - (- 14) \end{array}] + X = [\begin{array}{c} - 2 & - 5 \\ 13 & 7 \\ - 9 & 12 \end{array}] - [\begin{array}{c} 12 & 14 \\ 19 & 21 \\ 3 & - 14 \end{array}]$

Simplify $3 - 3$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & - 14 - (- 14) \end{array}] + X = [\begin{array}{c} - 2 & - 5 \\ 13 & 7 \\ - 9 & 12 \end{array}] - [\begin{array}{c} 12 & 14 \\ 19 & 21 \\ 3 & - 14 \end{array}]$

Simplify $- 14 - (- 14)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 2 & - 5 \\ 13 & 7 \\ - 9 & 12 \end{array}] - [\begin{array}{c} 12 & 14 \\ 19 & 21 \\ 3 & - 14 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 2 - 12 & - 5 - 14 \\ 13 - 19 & 7 - 21 \\ - 9 - 3 & 12 - (- 14) \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 2 - 12 & - 5 - 14 \\ 13 - 19 & 7 - 21 \\ - 9 - 3 & 12 - (- 14) \end{array}]$ .

Simplify $- 2 - 12$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 14 & - 5 - 14 \\ 13 - 19 & 7 - 21 \\ - 9 - 3 & 12 - (- 14) \end{array}]$

Simplify $- 5 - 14$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 14 & - 19 \\ 13 - 19 & 7 - 21 \\ - 9 - 3 & 12 - (- 14) \end{array}]$

Simplify $13 - 19$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 14 & - 19 \\ - 6 & 7 - 21 \\ - 9 - 3 & 12 - (- 14) \end{array}]$

Simplify $7 - 21$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 14 & - 19 \\ - 6 & - 14 \\ - 9 - 3 & 12 - (- 14) \end{array}]$

Simplify $- 9 - 3$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 14 & - 19 \\ - 6 & - 14 \\ - 12 & 12 - (- 14) \end{array}]$

Simplify $12 - (- 14)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 14 & - 19 \\ - 6 & - 14 \\ - 12 & 26 \end{array}]$

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

$X = [\begin{array}{c} - 14 & - 19 \\ - 6 & - 14 \\ - 12 & 26 \end{array}]$

The matrix is in the most simplified form.

$X = [\begin{array}{c} - 14 & - 19 \\ - 6 & - 14 \\ - 12 & 26 \end{array}]$

Solve the Matrix Equation x+[[12,14],[19,21],[3,-14]]=[[-2,-5],[13,7],[-9,12]]

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