Solve the Matrix Equation [[3,-8],[10,5]]-x=[[2,8],[-1,12]]

$[\begin{array}{c} 3 & - 8 \\ 10 & 5 \end{array}] - x = [\begin{array}{c} 2 & 8 \\ - 1 & 12 \end{array}]$

Step 1

Subtract the matrix from both sides of the equation.

$[\begin{array}{c} 3 & - 8 \\ 10 & 5 \end{array}] - X - [\begin{array}{c} 3 & - 8 \\ 10 & 5 \end{array}] = [\begin{array}{c} 2 & 8 \\ - 1 & 12 \end{array}] - [\begin{array}{c} 3 & - 8 \\ 10 & 5 \end{array}]$

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 3 - 3 & - 8 - (- 8) \\ 10 - 10 & 5 - 5 \end{array}] - X = [\begin{array}{c} 2 & 8 \\ - 1 & 12 \end{array}] - [\begin{array}{c} 3 & - 8 \\ 10 & 5 \end{array}]$

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

Simplify $3 - 3$ .

$[\begin{array}{c} 0 & - 8 - (- 8) \\ 10 - 10 & 5 - 5 \end{array}] - X = [\begin{array}{c} 2 & 8 \\ - 1 & 12 \end{array}] - [\begin{array}{c} 3 & - 8 \\ 10 & 5 \end{array}]$

Simplify $- 8 - (- 8)$ .

$[\begin{array}{c} 0 & 0 \\ 10 - 10 & 5 - 5 \end{array}] - X = [\begin{array}{c} 2 & 8 \\ - 1 & 12 \end{array}] - [\begin{array}{c} 3 & - 8 \\ 10 & 5 \end{array}]$

Simplify $10 - 10$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 5 - 5 \end{array}] - X = [\begin{array}{c} 2 & 8 \\ - 1 & 12 \end{array}] - [\begin{array}{c} 3 & - 8 \\ 10 & 5 \end{array}]$

Simplify $5 - 5$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} 2 & 8 \\ - 1 & 12 \end{array}] - [\begin{array}{c} 3 & - 8 \\ 10 & 5 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} 2 - 3 & 8 - (- 8) \\ - 1 - 10 & 12 - 5 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 2 - 3 & 8 - (- 8) \\ - 1 - 10 & 12 - 5 \end{array}]$ .

Simplify $2 - 3$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} - 1 & 8 - (- 8) \\ - 1 - 10 & 12 - 5 \end{array}]$

Simplify $8 - (- 8)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} - 1 & 16 \\ - 1 - 10 & 12 - 5 \end{array}]$

Simplify $- 1 - 10$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} - 1 & 16 \\ - 11 & 12 - 5 \end{array}]$

Simplify $12 - 5$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} - 1 & 16 \\ - 11 & 7 \end{array}]$

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

$- X = [\begin{array}{c} - 1 & 16 \\ - 11 & 7 \end{array}]$

Step 3

Multiply both sides of the equation by $- 1$ .

$- 1 \cdot (- X) = - 1 \cdot [\begin{array}{c} - 1 & 16 \\ - 11 & 7 \end{array}]$

Step 4

Simplify both sides of the equation.

Multiply $- 1 (- X)$ .

Multiply $- 1$ by $- 1$ .

$1 X = - 1 \cdot [\begin{array}{c} - 1 & 16 \\ - 11 & 7 \end{array}]$

Multiply $X$ by $1$ .

$X = - 1 \cdot [\begin{array}{c} - 1 & 16 \\ - 11 & 7 \end{array}]$

Simplify the right side of the equation.

Multiply $- 1$ by each element of the matrix.

$X = [\begin{array}{c} - 1 \cdot - 1 & - 1 \cdot 16 \\ - 1 \cdot - 11 & - 1 \cdot 7 \end{array}]$

Simplify each element in the matrix.

Rearrange $- 1 \cdot - 1$ .

$X = [\begin{array}{c} 1 & - 1 \cdot 16 \\ - 1 \cdot - 11 & - 1 \cdot 7 \end{array}]$

Rearrange $- 1 \cdot 16$ .

$X = [\begin{array}{c} 1 & - 16 \\ - 1 \cdot - 11 & - 1 \cdot 7 \end{array}]$

Rearrange $- 1 \cdot - 11$ .

$X = [\begin{array}{c} 1 & - 16 \\ 11 & - 1 \cdot 7 \end{array}]$

Rearrange $- 1 \cdot 7$ .

$X = [\begin{array}{c} 1 & - 16 \\ 11 & - 7 \end{array}]$

Solve the Matrix Equation [[3,-8],[10,5]]-x=[[2,8],[-1,12]]

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