Solve the Matrix Equation [[3,-8,0],[8,2,1]]+x=[[5,3,-9],[2,12,0]]

$[\begin{array}{c} 3 & - 8 & 0 \\ 8 & 2 & 1 \end{array}] + x = [\begin{array}{c} 5 & 3 & - 9 \\ 2 & 12 & 0 \end{array}]$

Step 1

Subtract the matrix from both sides of the equation.

$[\begin{array}{c} 3 & - 8 & 0 \\ 8 & 2 & 1 \end{array}] + X - [\begin{array}{c} 3 & - 8 & 0 \\ 8 & 2 & 1 \end{array}] = [\begin{array}{c} 5 & 3 & - 9 \\ 2 & 12 & 0 \end{array}] - [\begin{array}{c} 3 & - 8 & 0 \\ 8 & 2 & 1 \end{array}]$

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 3 - 3 & - 8 - (- 8) & 0 - 0 \\ 8 - 8 & 2 - 2 & 1 - 1 \end{array}] + X = [\begin{array}{c} 5 & 3 & - 9 \\ 2 & 12 & 0 \end{array}] - [\begin{array}{c} 3 & - 8 & 0 \\ 8 & 2 & 1 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 3 - 3 & - 8 - (- 8) & 0 - 0 \\ 8 - 8 & 2 - 2 & 1 - 1 \end{array}]$ .

Simplify $3 - 3$ .

$[\begin{array}{c} 0 & - 8 - (- 8) & 0 - 0 \\ 8 - 8 & 2 - 2 & 1 - 1 \end{array}] + X = [\begin{array}{c} 5 & 3 & - 9 \\ 2 & 12 & 0 \end{array}] - [\begin{array}{c} 3 & - 8 & 0 \\ 8 & 2 & 1 \end{array}]$

Simplify $- 8 - (- 8)$ .

$[\begin{array}{c} 0 & 0 & 0 - 0 \\ 8 - 8 & 2 - 2 & 1 - 1 \end{array}] + X = [\begin{array}{c} 5 & 3 & - 9 \\ 2 & 12 & 0 \end{array}] - [\begin{array}{c} 3 & - 8 & 0 \\ 8 & 2 & 1 \end{array}]$

Simplify $0 - 0$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 8 - 8 & 2 - 2 & 1 - 1 \end{array}] + X = [\begin{array}{c} 5 & 3 & - 9 \\ 2 & 12 & 0 \end{array}] - [\begin{array}{c} 3 & - 8 & 0 \\ 8 & 2 & 1 \end{array}]$

Simplify $8 - 8$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 2 - 2 & 1 - 1 \end{array}] + X = [\begin{array}{c} 5 & 3 & - 9 \\ 2 & 12 & 0 \end{array}] - [\begin{array}{c} 3 & - 8 & 0 \\ 8 & 2 & 1 \end{array}]$

Simplify $2 - 2$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 1 - 1 \end{array}] + X = [\begin{array}{c} 5 & 3 & - 9 \\ 2 & 12 & 0 \end{array}] - [\begin{array}{c} 3 & - 8 & 0 \\ 8 & 2 & 1 \end{array}]$

Simplify $1 - 1$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 5 & 3 & - 9 \\ 2 & 12 & 0 \end{array}] - [\begin{array}{c} 3 & - 8 & 0 \\ 8 & 2 & 1 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 5 - 3 & 3 - (- 8) & - 9 - 0 \\ 2 - 8 & 12 - 2 & 0 - 1 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 5 - 3 & 3 - (- 8) & - 9 - 0 \\ 2 - 8 & 12 - 2 & 0 - 1 \end{array}]$ .

Simplify $5 - 3$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & 3 - (- 8) & - 9 - 0 \\ 2 - 8 & 12 - 2 & 0 - 1 \end{array}]$

Simplify $3 - (- 8)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & 11 & - 9 - 0 \\ 2 - 8 & 12 - 2 & 0 - 1 \end{array}]$

Simplify $- 9 - 0$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & 11 & - 9 \\ 2 - 8 & 12 - 2 & 0 - 1 \end{array}]$

Simplify $2 - 8$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & 11 & - 9 \\ - 6 & 12 - 2 & 0 - 1 \end{array}]$

Simplify $12 - 2$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & 11 & - 9 \\ - 6 & 10 & 0 - 1 \end{array}]$

Simplify $0 - 1$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & 11 & - 9 \\ - 6 & 10 & - 1 \end{array}]$

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

$X = [\begin{array}{c} 2 & 11 & - 9 \\ - 6 & 10 & - 1 \end{array}]$

Step 3

The matrix is in the most simplified form.

$X = [\begin{array}{c} 2 & 11 & - 9 \\ - 6 & 10 & - 1 \end{array}]$

Solve the Matrix Equation [[3,-8,0],[8,2,1]]+x=[[5,3,-9],[2,12,0]]

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