Solve the Matrix Equation d+[[-1,-15],[0,7]]=[[8,-4],[-14,12]]

$d + [\begin{array}{c} - 1 & - 15 \\ 0 & 7 \end{array}] = [\begin{array}{c} 8 & - 4 \\ - 14 & 12 \end{array}]$

Step 1

Subtract the matrix from both sides of the equation.

$X + [\begin{array}{c} - 1 & - 15 \\ 0 & 7 \end{array}] - [\begin{array}{c} - 1 & - 15 \\ 0 & 7 \end{array}] = [\begin{array}{c} 8 & - 4 \\ - 14 & 12 \end{array}] - [\begin{array}{c} - 1 & - 15 \\ 0 & 7 \end{array}]$

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} - 1 - (- 1) & - 15 - (- 15) \\ 0 - 0 & 7 - 7 \end{array}] + X = [\begin{array}{c} 8 & - 4 \\ - 14 & 12 \end{array}] - [\begin{array}{c} - 1 & - 15 \\ 0 & 7 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 1 - (- 1) & - 15 - (- 15) \\ 0 - 0 & 7 - 7 \end{array}]$ .

Simplify $- 1 - (- 1)$ .

$[\begin{array}{c} 0 & - 15 - (- 15) \\ 0 - 0 & 7 - 7 \end{array}] + X = [\begin{array}{c} 8 & - 4 \\ - 14 & 12 \end{array}] - [\begin{array}{c} - 1 & - 15 \\ 0 & 7 \end{array}]$

Simplify $- 15 - (- 15)$ .

$[\begin{array}{c} 0 & 0 \\ 0 - 0 & 7 - 7 \end{array}] + X = [\begin{array}{c} 8 & - 4 \\ - 14 & 12 \end{array}] - [\begin{array}{c} - 1 & - 15 \\ 0 & 7 \end{array}]$

Simplify $0 - 0$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 7 - 7 \end{array}] + X = [\begin{array}{c} 8 & - 4 \\ - 14 & 12 \end{array}] - [\begin{array}{c} - 1 & - 15 \\ 0 & 7 \end{array}]$

Simplify $7 - 7$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & - 4 \\ - 14 & 12 \end{array}] - [\begin{array}{c} - 1 & - 15 \\ 0 & 7 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 8 - (- 1) & - 4 - (- 15) \\ - 14 - 0 & 12 - 7 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 8 - (- 1) & - 4 - (- 15) \\ - 14 - 0 & 12 - 7 \end{array}]$ .

Simplify $8 - (- 1)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 9 & - 4 - (- 15) \\ - 14 - 0 & 12 - 7 \end{array}]$

Simplify $- 4 - (- 15)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 9 & 11 \\ - 14 - 0 & 12 - 7 \end{array}]$

Simplify $- 14 - 0$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 9 & 11 \\ - 14 & 12 - 7 \end{array}]$

Simplify $12 - 7$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 9 & 11 \\ - 14 & 5 \end{array}]$

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

$X = [\begin{array}{c} 9 & 11 \\ - 14 & 5 \end{array}]$

Step 3

The matrix is in the most simplified form.

$X = [\begin{array}{c} 9 & 11 \\ - 14 & 5 \end{array}]$

Solve the Matrix Equation d+[[-1,-15],[0,7]]=[[8,-4],[-14,12]]

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