Solve the Matrix Equation [[5,5,-7],[2,3,-6]]+X=[[1,1,5],[4,-2,9]]

$[\begin{array}{c} 5 & 5 & - 7 \\ 2 & 3 & - 6 \end{array}] + X = [\begin{array}{c} 1 & 1 & 5 \\ 4 & - 2 & 9 \end{array}]$

Step 1

Subtract the matrix from both sides of the equation.

$[\begin{array}{c} 5 & 5 & - 7 \\ 2 & 3 & - 6 \end{array}] + X - [\begin{array}{c} 5 & 5 & - 7 \\ 2 & 3 & - 6 \end{array}] = [\begin{array}{c} 1 & 1 & 5 \\ 4 & - 2 & 9 \end{array}] - [\begin{array}{c} 5 & 5 & - 7 \\ 2 & 3 & - 6 \end{array}]$

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 5 - 5 & 5 - 5 & - 7 - (- 7) \\ 2 - 2 & 3 - 3 & - 6 - (- 6) \end{array}] + X = [\begin{array}{c} 1 & 1 & 5 \\ 4 & - 2 & 9 \end{array}] - [\begin{array}{c} 5 & 5 & - 7 \\ 2 & 3 & - 6 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 5 - 5 & 5 - 5 & - 7 - (- 7) \\ 2 - 2 & 3 - 3 & - 6 - (- 6) \end{array}]$ .

Simplify $5 - 5$ .

$[\begin{array}{c} 0 & 5 - 5 & - 7 - (- 7) \\ 2 - 2 & 3 - 3 & - 6 - (- 6) \end{array}] + X = [\begin{array}{c} 1 & 1 & 5 \\ 4 & - 2 & 9 \end{array}] - [\begin{array}{c} 5 & 5 & - 7 \\ 2 & 3 & - 6 \end{array}]$

Simplify $5 - 5$ .

$[\begin{array}{c} 0 & 0 & - 7 - (- 7) \\ 2 - 2 & 3 - 3 & - 6 - (- 6) \end{array}] + X = [\begin{array}{c} 1 & 1 & 5 \\ 4 & - 2 & 9 \end{array}] - [\begin{array}{c} 5 & 5 & - 7 \\ 2 & 3 & - 6 \end{array}]$

Simplify $- 7 - (- 7)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 2 - 2 & 3 - 3 & - 6 - (- 6) \end{array}] + X = [\begin{array}{c} 1 & 1 & 5 \\ 4 & - 2 & 9 \end{array}] - [\begin{array}{c} 5 & 5 & - 7 \\ 2 & 3 & - 6 \end{array}]$

Simplify $2 - 2$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 3 - 3 & - 6 - (- 6) \end{array}] + X = [\begin{array}{c} 1 & 1 & 5 \\ 4 & - 2 & 9 \end{array}] - [\begin{array}{c} 5 & 5 & - 7 \\ 2 & 3 & - 6 \end{array}]$

Simplify $3 - 3$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & - 6 - (- 6) \end{array}] + X = [\begin{array}{c} 1 & 1 & 5 \\ 4 & - 2 & 9 \end{array}] - [\begin{array}{c} 5 & 5 & - 7 \\ 2 & 3 & - 6 \end{array}]$

Simplify $- 6 - (- 6)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 1 & 1 & 5 \\ 4 & - 2 & 9 \end{array}] - [\begin{array}{c} 5 & 5 & - 7 \\ 2 & 3 & - 6 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 1 - 5 & 1 - 5 & 5 - (- 7) \\ 4 - 2 & - 2 - 3 & 9 - (- 6) \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 1 - 5 & 1 - 5 & 5 - (- 7) \\ 4 - 2 & - 2 - 3 & 9 - (- 6) \end{array}]$ .

Simplify $1 - 5$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 4 & 1 - 5 & 5 - (- 7) \\ 4 - 2 & - 2 - 3 & 9 - (- 6) \end{array}]$

Simplify $1 - 5$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 4 & - 4 & 5 - (- 7) \\ 4 - 2 & - 2 - 3 & 9 - (- 6) \end{array}]$

Simplify $5 - (- 7)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 4 & - 4 & 12 \\ 4 - 2 & - 2 - 3 & 9 - (- 6) \end{array}]$

Simplify $4 - 2$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 4 & - 4 & 12 \\ 2 & - 2 - 3 & 9 - (- 6) \end{array}]$

Simplify $- 2 - 3$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 4 & - 4 & 12 \\ 2 & - 5 & 9 - (- 6) \end{array}]$

Simplify $9 - (- 6)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} - 4 & - 4 & 12 \\ 2 & - 5 & 15 \end{array}]$

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

$X = [\begin{array}{c} - 4 & - 4 & 12 \\ 2 & - 5 & 15 \end{array}]$

Step 3

The matrix is in the most simplified form.

$X = [\begin{array}{c} - 4 & - 4 & 12 \\ 2 & - 5 & 15 \end{array}]$

Solve the Matrix Equation [[5,5,-7],[2,3,-6]]+X=[[1,1,5],[4,-2,9]]

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