Solve the Matrix Equation 1/4x-[[8,1,1],[2,5,9]]=[[7,3,9],[22,-15,9]]

$\frac{1}{4} x - [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}] = [\begin{array}{c} 7 & 3 & 9 \\ 22 & - 15 & 9 \end{array}]$

Add the matrix to both sides of the equation.

$\frac{1}{4} X - [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}] + [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}] = [\begin{array}{c} 7 & 3 & 9 \\ 22 & - 15 & 9 \end{array}] + [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}]$

Simplify both sides of the equation.

Simplify the left side of the equation.

Combine $\frac{1}{4}$ and $X$ .

$- [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}] + [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}] + \frac{X}{4} = [\begin{array}{c} 7 & 3 & 9 \\ 22 & - 15 & 9 \end{array}] + [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}]$

Add the corresponding elements.

$[\begin{array}{c} - 8 + 8 & - 1 + 1 & - 1 + 1 \\ - 2 + 2 & - 5 + 5 & - 9 + 9 \end{array}] + \frac{X}{4} = [\begin{array}{c} 7 & 3 & 9 \\ 22 & - 15 & 9 \end{array}] + [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}]$

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

Simplify $- 8 + 8$ .

$[\begin{array}{c} 0 & - 1 + 1 & - 1 + 1 \\ - 2 + 2 & - 5 + 5 & - 9 + 9 \end{array}] + \frac{X}{4} = [\begin{array}{c} 7 & 3 & 9 \\ 22 & - 15 & 9 \end{array}] + [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}]$

Simplify $- 1 + 1$ .

$[\begin{array}{c} 0 & 0 & - 1 + 1 \\ - 2 + 2 & - 5 + 5 & - 9 + 9 \end{array}] + \frac{X}{4} = [\begin{array}{c} 7 & 3 & 9 \\ 22 & - 15 & 9 \end{array}] + [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}]$

Simplify $- 1 + 1$ .

$[\begin{array}{c} 0 & 0 & 0 \\ - 2 + 2 & - 5 + 5 & - 9 + 9 \end{array}] + \frac{X}{4} = [\begin{array}{c} 7 & 3 & 9 \\ 22 & - 15 & 9 \end{array}] + [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}]$

Simplify $- 2 + 2$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & - 5 + 5 & - 9 + 9 \end{array}] + \frac{X}{4} = [\begin{array}{c} 7 & 3 & 9 \\ 22 & - 15 & 9 \end{array}] + [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}]$

Simplify $- 5 + 5$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & - 9 + 9 \end{array}] + \frac{X}{4} = [\begin{array}{c} 7 & 3 & 9 \\ 22 & - 15 & 9 \end{array}] + [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}]$

Simplify $- 9 + 9$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{4} = [\begin{array}{c} 7 & 3 & 9 \\ 22 & - 15 & 9 \end{array}] + [\begin{array}{c} 8 & 1 & 1 \\ 2 & 5 & 9 \end{array}]$

Simplify the right side of the equation.

Add the corresponding elements.

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{4} = [\begin{array}{c} 7 + 8 & 3 + 1 & 9 + 1 \\ 22 + 2 & - 15 + 5 & 9 + 9 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 7 + 8 & 3 + 1 & 9 + 1 \\ 22 + 2 & - 15 + 5 & 9 + 9 \end{array}]$ .

Simplify $7 + 8$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{4} = [\begin{array}{c} 15 & 3 + 1 & 9 + 1 \\ 22 + 2 & - 15 + 5 & 9 + 9 \end{array}]$

Simplify $3 + 1$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{4} = [\begin{array}{c} 15 & 4 & 9 + 1 \\ 22 + 2 & - 15 + 5 & 9 + 9 \end{array}]$

Simplify $9 + 1$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{4} = [\begin{array}{c} 15 & 4 & 10 \\ 22 + 2 & - 15 + 5 & 9 + 9 \end{array}]$

Simplify $22 + 2$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{4} = [\begin{array}{c} 15 & 4 & 10 \\ 24 & - 15 + 5 & 9 + 9 \end{array}]$

Simplify $- 15 + 5$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{4} = [\begin{array}{c} 15 & 4 & 10 \\ 24 & - 10 & 9 + 9 \end{array}]$

Simplify $9 + 9$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{4} = [\begin{array}{c} 15 & 4 & 10 \\ 24 & - 10 & 18 \end{array}]$

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

$\frac{X}{4} = [\begin{array}{c} 15 & 4 & 10 \\ 24 & - 10 & 18 \end{array}]$

Multiply both sides of the equation by $4$ .

$4 \cdot \frac{X}{4} = 4 \cdot [\begin{array}{c} 15 & 4 & 10 \\ 24 & - 10 & 18 \end{array}]$

Simplify both sides of the equation.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \cdot \frac{X}{4} = 4 \cdot [\begin{array}{c} 15 & 4 & 10 \\ 24 & - 10 & 18 \end{array}]$

Rewrite the expression.

$X = 4 \cdot [\begin{array}{c} 15 & 4 & 10 \\ 24 & - 10 & 18 \end{array}]$

Simplify the right side of the equation.

Multiply $4$ by each element of the matrix.

$X = [\begin{array}{c} 4 \cdot 15 & 4 \cdot 4 & 4 \cdot 10 \\ 4 \cdot 24 & 4 \cdot - 10 & 4 \cdot 18 \end{array}]$

Simplify each element in the matrix.

Rearrange $4 \cdot 15$ .

$X = [\begin{array}{c} 60 & 4 \cdot 4 & 4 \cdot 10 \\ 4 \cdot 24 & 4 \cdot - 10 & 4 \cdot 18 \end{array}]$

Rearrange $4 \cdot 4$ .

$X = [\begin{array}{c} 60 & 16 & 4 \cdot 10 \\ 4 \cdot 24 & 4 \cdot - 10 & 4 \cdot 18 \end{array}]$

Rearrange $4 \cdot 10$ .

$X = [\begin{array}{c} 60 & 16 & 40 \\ 4 \cdot 24 & 4 \cdot - 10 & 4 \cdot 18 \end{array}]$

Rearrange $4 \cdot 24$ .

$X = [\begin{array}{c} 60 & 16 & 40 \\ 96 & 4 \cdot - 10 & 4 \cdot 18 \end{array}]$

Rearrange $4 \cdot - 10$ .

$X = [\begin{array}{c} 60 & 16 & 40 \\ 96 & - 40 & 4 \cdot 18 \end{array}]$

Rearrange $4 \cdot 18$ .

$X = [\begin{array}{c} 60 & 16 & 40 \\ 96 & - 40 & 72 \end{array}]$

Solve the Matrix Equation 1/4x-[[8,1,1],[2,5,9]]=[[7,3,9],[22,-15,9]]

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