Solve the Matrix Equation X-[[6,-7],[8,-5],[2,10]]=[[7,-22],[3,16],[12,9]]

$X - [\begin{array}{c} 6 & - 7 \\ 8 & - 5 \\ 2 & 10 \end{array}] = [\begin{array}{c} 7 & - 22 \\ 3 & 16 \\ 12 & 9 \end{array}]$

Add the matrix to both sides of the equation.

$X - [\begin{array}{c} 6 & - 7 \\ 8 & - 5 \\ 2 & 10 \end{array}] + [\begin{array}{c} 6 & - 7 \\ 8 & - 5 \\ 2 & 10 \end{array}] = [\begin{array}{c} 7 & - 22 \\ 3 & 16 \\ 12 & 9 \end{array}] + [\begin{array}{c} 6 & - 7 \\ 8 & - 5 \\ 2 & 10 \end{array}]$

Simplify both sides of the equation.

Simplify the left side of the equation.

Add the corresponding elements.

$[\begin{array}{c} - 6 + 6 & 7 - 7 \\ - 8 + 8 & 5 - 5 \\ - 2 + 2 & - 10 + 10 \end{array}] + X = [\begin{array}{c} 7 & - 22 \\ 3 & 16 \\ 12 & 9 \end{array}] + [\begin{array}{c} 6 & - 7 \\ 8 & - 5 \\ 2 & 10 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 6 + 6 & 7 - 7 \\ - 8 + 8 & 5 - 5 \\ - 2 + 2 & - 10 + 10 \end{array}]$ .

Simplify $- 6 + 6$ .

$[\begin{array}{c} 0 & 7 - 7 \\ - 8 + 8 & 5 - 5 \\ - 2 + 2 & - 10 + 10 \end{array}] + X = [\begin{array}{c} 7 & - 22 \\ 3 & 16 \\ 12 & 9 \end{array}] + [\begin{array}{c} 6 & - 7 \\ 8 & - 5 \\ 2 & 10 \end{array}]$

Simplify $7 - 7$ .

$[\begin{array}{c} 0 & 0 \\ - 8 + 8 & 5 - 5 \\ - 2 + 2 & - 10 + 10 \end{array}] + X = [\begin{array}{c} 7 & - 22 \\ 3 & 16 \\ 12 & 9 \end{array}] + [\begin{array}{c} 6 & - 7 \\ 8 & - 5 \\ 2 & 10 \end{array}]$

Simplify $- 8 + 8$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 5 - 5 \\ - 2 + 2 & - 10 + 10 \end{array}] + X = [\begin{array}{c} 7 & - 22 \\ 3 & 16 \\ 12 & 9 \end{array}] + [\begin{array}{c} 6 & - 7 \\ 8 & - 5 \\ 2 & 10 \end{array}]$

Simplify $5 - 5$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ - 2 + 2 & - 10 + 10 \end{array}] + X = [\begin{array}{c} 7 & - 22 \\ 3 & 16 \\ 12 & 9 \end{array}] + [\begin{array}{c} 6 & - 7 \\ 8 & - 5 \\ 2 & 10 \end{array}]$

Simplify $- 2 + 2$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & - 10 + 10 \end{array}] + X = [\begin{array}{c} 7 & - 22 \\ 3 & 16 \\ 12 & 9 \end{array}] + [\begin{array}{c} 6 & - 7 \\ 8 & - 5 \\ 2 & 10 \end{array}]$

Simplify $- 10 + 10$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 7 & - 22 \\ 3 & 16 \\ 12 & 9 \end{array}] + [\begin{array}{c} 6 & - 7 \\ 8 & - 5 \\ 2 & 10 \end{array}]$

Simplify the right side of the equation.

Add the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 7 + 6 & - 22 - 7 \\ 3 + 8 & 16 - 5 \\ 12 + 2 & 9 + 10 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 7 + 6 & - 22 - 7 \\ 3 + 8 & 16 - 5 \\ 12 + 2 & 9 + 10 \end{array}]$ .

Simplify $7 + 6$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 13 & - 22 - 7 \\ 3 + 8 & 16 - 5 \\ 12 + 2 & 9 + 10 \end{array}]$

Simplify $- 22 - 7$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 13 & - 29 \\ 3 + 8 & 16 - 5 \\ 12 + 2 & 9 + 10 \end{array}]$

Simplify $3 + 8$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 13 & - 29 \\ 11 & 16 - 5 \\ 12 + 2 & 9 + 10 \end{array}]$

Simplify $16 - 5$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 13 & - 29 \\ 11 & 11 \\ 12 + 2 & 9 + 10 \end{array}]$

Simplify $12 + 2$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 13 & - 29 \\ 11 & 11 \\ 14 & 9 + 10 \end{array}]$

Simplify $9 + 10$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 13 & - 29 \\ 11 & 11 \\ 14 & 19 \end{array}]$

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

$X = [\begin{array}{c} 13 & - 29 \\ 11 & 11 \\ 14 & 19 \end{array}]$

The matrix is in the most simplified form.

$X = [\begin{array}{c} 13 & - 29 \\ 11 & 11 \\ 14 & 19 \end{array}]$

Solve the Matrix Equation X-[[6,-7],[8,-5],[2,10]]=[[7,-22],[3,16],[12,9]]

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