Solve the Matrix Equation 1/9x+[[-21,-25,-8],[3,4,7]]=[[-24,-30,-11],[8,-1,0]]

$\frac{1}{9} x + [\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}] = [\begin{array}{c} - 24 & - 30 & - 11 \\ 8 & - 1 & 0 \end{array}]$

Step 1

Subtract the matrix from both sides of the equation.

$\frac{1}{9} X + [\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}] - [\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}] = [\begin{array}{c} - 24 & - 30 & - 11 \\ 8 & - 1 & 0 \end{array}] - [\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}]$

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Combine $\frac{1}{9}$ and $X$ .

$[\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}] - [\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}] + \frac{X}{9} = [\begin{array}{c} - 24 & - 30 & - 11 \\ 8 & - 1 & 0 \end{array}] - [\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}]$

Subtract the corresponding elements.

$[\begin{array}{c} - 21 - (- 21) & - 25 - (- 25) & - 8 - (- 8) \\ 3 - 3 & 4 - 4 & 7 - 7 \end{array}] + \frac{X}{9} = [\begin{array}{c} - 24 & - 30 & - 11 \\ 8 & - 1 & 0 \end{array}] - [\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 21 - (- 21) & - 25 - (- 25) & - 8 - (- 8) \\ 3 - 3 & 4 - 4 & 7 - 7 \end{array}]$ .

Simplify $- 21 - (- 21)$ .

$[\begin{array}{c} 0 & - 25 - (- 25) & - 8 - (- 8) \\ 3 - 3 & 4 - 4 & 7 - 7 \end{array}] + \frac{X}{9} = [\begin{array}{c} - 24 & - 30 & - 11 \\ 8 & - 1 & 0 \end{array}] - [\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}]$

Simplify $- 25 - (- 25)$ .

$[\begin{array}{c} 0 & 0 & - 8 - (- 8) \\ 3 - 3 & 4 - 4 & 7 - 7 \end{array}] + \frac{X}{9} = [\begin{array}{c} - 24 & - 30 & - 11 \\ 8 & - 1 & 0 \end{array}] - [\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}]$

Simplify $- 8 - (- 8)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 3 - 3 & 4 - 4 & 7 - 7 \end{array}] + \frac{X}{9} = [\begin{array}{c} - 24 & - 30 & - 11 \\ 8 & - 1 & 0 \end{array}] - [\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}]$

Simplify $3 - 3$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 4 - 4 & 7 - 7 \end{array}] + \frac{X}{9} = [\begin{array}{c} - 24 & - 30 & - 11 \\ 8 & - 1 & 0 \end{array}] - [\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}]$

Simplify $4 - 4$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 7 - 7 \end{array}] + \frac{X}{9} = [\begin{array}{c} - 24 & - 30 & - 11 \\ 8 & - 1 & 0 \end{array}] - [\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}]$

Simplify $7 - 7$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{9} = [\begin{array}{c} - 24 & - 30 & - 11 \\ 8 & - 1 & 0 \end{array}] - [\begin{array}{c} - 21 & - 25 & - 8 \\ 3 & 4 & 7 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{9} = [\begin{array}{c} - 24 - (- 21) & - 30 - (- 25) & - 11 - (- 8) \\ 8 - 3 & - 1 - 4 & 0 - 7 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 24 - (- 21) & - 30 - (- 25) & - 11 - (- 8) \\ 8 - 3 & - 1 - 4 & 0 - 7 \end{array}]$ .

Simplify $- 24 - (- 21)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{9} = [\begin{array}{c} - 3 & - 30 - (- 25) & - 11 - (- 8) \\ 8 - 3 & - 1 - 4 & 0 - 7 \end{array}]$

Simplify $- 30 - (- 25)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{9} = [\begin{array}{c} - 3 & - 5 & - 11 - (- 8) \\ 8 - 3 & - 1 - 4 & 0 - 7 \end{array}]$

Simplify $- 11 - (- 8)$ .

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

Simplify $8 - 3$ .

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

Simplify $- 1 - 4$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{9} = [\begin{array}{c} - 3 & - 5 & - 3 \\ 5 & - 5 & 0 - 7 \end{array}]$

Simplify $0 - 7$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + \frac{X}{9} = [\begin{array}{c} - 3 & - 5 & - 3 \\ 5 & - 5 & - 7 \end{array}]$

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

$\frac{X}{9} = [\begin{array}{c} - 3 & - 5 & - 3 \\ 5 & - 5 & - 7 \end{array}]$

Step 3

Multiply both sides of the equation by $9$ .

$9 \cdot \frac{X}{9} = 9 \cdot [\begin{array}{c} - 3 & - 5 & - 3 \\ 5 & - 5 & - 7 \end{array}]$

Step 4

Simplify both sides of the equation.

Cancel the common factor of $9$ .

Cancel the common factor.

$9 \cdot \frac{X}{9} = 9 \cdot [\begin{array}{c} - 3 & - 5 & - 3 \\ 5 & - 5 & - 7 \end{array}]$

Rewrite the expression.

$X = 9 \cdot [\begin{array}{c} - 3 & - 5 & - 3 \\ 5 & - 5 & - 7 \end{array}]$

Simplify the right side of the equation.

Multiply $9$ by each element of the matrix.

$X = [\begin{array}{c} 9 \cdot - 3 & 9 \cdot - 5 & 9 \cdot - 3 \\ 9 \cdot 5 & 9 \cdot - 5 & 9 \cdot - 7 \end{array}]$

Simplify each element in the matrix.

Rearrange $9 \cdot - 3$ .

$X = [\begin{array}{c} - 27 & 9 \cdot - 5 & 9 \cdot - 3 \\ 9 \cdot 5 & 9 \cdot - 5 & 9 \cdot - 7 \end{array}]$

Rearrange $9 \cdot - 5$ .

$X = [\begin{array}{c} - 27 & - 45 & 9 \cdot - 3 \\ 9 \cdot 5 & 9 \cdot - 5 & 9 \cdot - 7 \end{array}]$

Rearrange $9 \cdot - 3$ .

$X = [\begin{array}{c} - 27 & - 45 & - 27 \\ 9 \cdot 5 & 9 \cdot - 5 & 9 \cdot - 7 \end{array}]$

Rearrange $9 \cdot 5$ .

$X = [\begin{array}{c} - 27 & - 45 & - 27 \\ 45 & 9 \cdot - 5 & 9 \cdot - 7 \end{array}]$

Rearrange $9 \cdot - 5$ .

$X = [\begin{array}{c} - 27 & - 45 & - 27 \\ 45 & - 45 & 9 \cdot - 7 \end{array}]$

Rearrange $9 \cdot - 7$ .

$X = [\begin{array}{c} - 27 & - 45 & - 27 \\ 45 & - 45 & - 63 \end{array}]$

Solve the Matrix Equation 1/9x+[[-21,-25,-8],[3,4,7]]=[[-24,-30,-11],[8,-1,0]]

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