Solve the Matrix Equation 3x+[[-1,1,0],[8,-5,9],[4,3,-1]]=[[11,4,9],[2,-17,0],[-14,-12,5]]

$3 x + [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}] = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}]$

Subtract the matrix from both sides of the equation.

$3 X + [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}] - [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}] = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}] - [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}]$

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} - 1 - (- 1) & 1 - 1 & 0 - 0 \\ 8 - 8 & - 5 - (- 5) & 9 - 9 \\ 4 - 4 & 3 - 3 & - 1 - (- 1) \end{array}] + 3 X = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}] - [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 1 - (- 1) & 1 - 1 & 0 - 0 \\ 8 - 8 & - 5 - (- 5) & 9 - 9 \\ 4 - 4 & 3 - 3 & - 1 - (- 1) \end{array}]$ .

Simplify $- 1 - (- 1)$ .

$[\begin{array}{c} 0 & 1 - 1 & 0 - 0 \\ 8 - 8 & - 5 - (- 5) & 9 - 9 \\ 4 - 4 & 3 - 3 & - 1 - (- 1) \end{array}] + 3 X = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}] - [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}]$

Simplify $1 - 1$ .

$[\begin{array}{c} 0 & 0 & 0 - 0 \\ 8 - 8 & - 5 - (- 5) & 9 - 9 \\ 4 - 4 & 3 - 3 & - 1 - (- 1) \end{array}] + 3 X = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}] - [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}]$

Simplify $0 - 0$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 8 - 8 & - 5 - (- 5) & 9 - 9 \\ 4 - 4 & 3 - 3 & - 1 - (- 1) \end{array}] + 3 X = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}] - [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}]$

Simplify $8 - 8$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & - 5 - (- 5) & 9 - 9 \\ 4 - 4 & 3 - 3 & - 1 - (- 1) \end{array}] + 3 X = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}] - [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}]$

Simplify $- 5 - (- 5)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 9 - 9 \\ 4 - 4 & 3 - 3 & - 1 - (- 1) \end{array}] + 3 X = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}] - [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}]$

Simplify $9 - 9$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 4 - 4 & 3 - 3 & - 1 - (- 1) \end{array}] + 3 X = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}] - [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}]$

Simplify $4 - 4$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 3 - 3 & - 1 - (- 1) \end{array}] + 3 X = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}] - [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}]$

Simplify $3 - 3$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & - 1 - (- 1) \end{array}] + 3 X = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}] - [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}]$

Simplify $- 1 - (- 1)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}] - [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 11 - (- 1) & 4 - 1 & 9 - 0 \\ 2 - 8 & - 17 - (- 5) & 0 - 9 \\ - 14 - 4 & - 12 - 3 & 5 - (- 1) \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 11 - (- 1) & 4 - 1 & 9 - 0 \\ 2 - 8 & - 17 - (- 5) & 0 - 9 \\ - 14 - 4 & - 12 - 3 & 5 - (- 1) \end{array}]$ .

Simplify $11 - (- 1)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 12 & 4 - 1 & 9 - 0 \\ 2 - 8 & - 17 - (- 5) & 0 - 9 \\ - 14 - 4 & - 12 - 3 & 5 - (- 1) \end{array}]$

Simplify $4 - 1$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 12 & 3 & 9 - 0 \\ 2 - 8 & - 17 - (- 5) & 0 - 9 \\ - 14 - 4 & - 12 - 3 & 5 - (- 1) \end{array}]$

Simplify $9 - 0$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 12 & 3 & 9 \\ 2 - 8 & - 17 - (- 5) & 0 - 9 \\ - 14 - 4 & - 12 - 3 & 5 - (- 1) \end{array}]$

Simplify $2 - 8$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 17 - (- 5) & 0 - 9 \\ - 14 - 4 & - 12 - 3 & 5 - (- 1) \end{array}]$

Simplify $- 17 - (- 5)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & 0 - 9 \\ - 14 - 4 & - 12 - 3 & 5 - (- 1) \end{array}]$

Simplify $0 - 9$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 14 - 4 & - 12 - 3 & 5 - (- 1) \end{array}]$

Simplify $- 14 - 4$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 12 - 3 & 5 - (- 1) \end{array}]$

Simplify $- 12 - 3$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 15 & 5 - (- 1) \end{array}]$

Simplify $5 - (- 1)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 15 & 6 \end{array}]$

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

$3 X = [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 15 & 6 \end{array}]$

Multiply both sides of the equation by $\frac{1}{3}$ .

$\frac{1}{3} \cdot (3 X) = \frac{1}{3} \cdot [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 15 & 6 \end{array}]$

Simplify both sides of the equation.

Cancel the common factor of $3$ .

Factor $3$ out of $3 X$ .

$\frac{1}{3} \cdot (3 (X)) = \frac{1}{3} \cdot [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 15 & 6 \end{array}]$

Cancel the common factor.

$\frac{1}{3} \cdot (3 X) = \frac{1}{3} \cdot [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 15 & 6 \end{array}]$

Rewrite the expression.

$X = \frac{1}{3} \cdot [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 15 & 6 \end{array}]$

Simplify the right side of the equation.

Multiply $\frac{1}{3}$ by each element of the matrix.

$X = [\begin{array}{c} \frac{1}{3} \cdot 12 & \frac{1}{3} \cdot 3 & \frac{1}{3} \cdot 9 \\ \frac{1}{3} \cdot - 6 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Simplify each element in the matrix.

Rearrange $\frac{1}{3} \cdot 12$ .

$X = [\begin{array}{c} 4 & \frac{1}{3} \cdot 3 & \frac{1}{3} \cdot 9 \\ \frac{1}{3} \cdot - 6 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Rearrange $\frac{1}{3} \cdot 3$ .

$X = [\begin{array}{c} 4 & 1 & \frac{1}{3} \cdot 9 \\ \frac{1}{3} \cdot - 6 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Rearrange $\frac{1}{3} \cdot 9$ .

$X = [\begin{array}{c} 4 & 1 & 3 \\ \frac{1}{3} \cdot - 6 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Rearrange $\frac{1}{3} \cdot - 6$ .

$X = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Rearrange $\frac{1}{3} \cdot - 12$ .

$X = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & - 4 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Rearrange $\frac{1}{3} \cdot - 9$ .

$X = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & - 4 & - 3 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Rearrange $\frac{1}{3} \cdot - 18$ .

$X = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & - 4 & - 3 \\ - 6 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Rearrange $\frac{1}{3} \cdot - 15$ .

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

Rearrange $\frac{1}{3} \cdot 6$ .

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

Solve the Matrix Equation 3x+[[-1,1,0],[8,-5,9],[4,3,-1]]=[[11,4,9],[2,-17,0],[-14,-12,5]]

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