Solve the Matrix Equation -4X-[[-8,-17,4],[-16,-29,17]]=[[-24,-3,-16],[12,-3,15]]

$- 4 X - [\begin{array}{c} - 8 & - 17 & 4 \\ - 16 & - 29 & 17 \end{array}] = [\begin{array}{c} - 24 & - 3 & - 16 \\ 12 & - 3 & 15 \end{array}]$

Step 1

Move all terms not containing a variable to the right side.

Add $[\begin{array}{c} - 8 & - 17 & 4 \\ - 16 & - 29 & 17 \end{array}]$ to both sides of the equation.

$- 4 X = [\begin{array}{c} - 24 & - 3 & - 16 \\ 12 & - 3 & 15 \end{array}] + [\begin{array}{c} - 8 & - 17 & 4 \\ - 16 & - 29 & 17 \end{array}]$

Step 2

Simplify the right side.

Add the corresponding elements.

$- 4 X = [\begin{array}{c} - 24 - 8 & - 3 - 17 & - 16 + 4 \\ 12 - 16 & - 3 - 29 & 15 + 17 \end{array}]$

Simplify each element.

Subtract $8$ from $- 24$ .

$- 4 X = [\begin{array}{c} - 32 & - 3 - 17 & - 16 + 4 \\ 12 - 16 & - 3 - 29 & 15 + 17 \end{array}]$

Subtract $17$ from $- 3$ .

$- 4 X = [\begin{array}{c} - 32 & - 20 & - 16 + 4 \\ 12 - 16 & - 3 - 29 & 15 + 17 \end{array}]$

Add $- 16$ and $4$ .

$- 4 X = [\begin{array}{c} - 32 & - 20 & - 12 \\ 12 - 16 & - 3 - 29 & 15 + 17 \end{array}]$

Subtract $16$ from $12$ .

$- 4 X = [\begin{array}{c} - 32 & - 20 & - 12 \\ - 4 & - 3 - 29 & 15 + 17 \end{array}]$

Subtract $29$ from $- 3$ .

$- 4 X = [\begin{array}{c} - 32 & - 20 & - 12 \\ - 4 & - 32 & 15 + 17 \end{array}]$

Add $15$ and $17$ .

$- 4 X = [\begin{array}{c} - 32 & - 20 & - 12 \\ - 4 & - 32 & 32 \end{array}]$

Step 3

Multiply both sides by $- \frac{1}{4}$ .

$- \frac{1}{4} (- 4 X) = - \frac{1}{4} [\begin{array}{c} - 32 & - 20 & - 12 \\ - 4 & - 32 & 32 \end{array}]$

Step 4

Simplify.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{- 1}{4} (- 4 X) = - \frac{1}{4} [\begin{array}{c} - 32 & - 20 & - 12 \\ - 4 & - 32 & 32 \end{array}]$

Factor $4$ out of $- 4 X$ .

$\frac{- 1}{4} (4 (- X)) = - \frac{1}{4} [\begin{array}{c} - 32 & - 20 & - 12 \\ - 4 & - 32 & 32 \end{array}]$

Cancel the common factor.

$\frac{- 1}{4} (4 (- X)) = - \frac{1}{4} [\begin{array}{c} - 32 & - 20 & - 12 \\ - 4 & - 32 & 32 \end{array}]$

Rewrite the expression.

$- - X = - \frac{1}{4} [\begin{array}{c} - 32 & - 20 & - 12 \\ - 4 & - 32 & 32 \end{array}]$

Multiply $- 1$ by $- 1$ .

$1 X = - \frac{1}{4} [\begin{array}{c} - 32 & - 20 & - 12 \\ - 4 & - 32 & 32 \end{array}]$

Multiply $X$ by $1$ .

$X = - \frac{1}{4} [\begin{array}{c} - 32 & - 20 & - 12 \\ - 4 & - 32 & 32 \end{array}]$

Multiply $- \frac{1}{4}$ by each element of the matrix.

$X = [\begin{array}{c} - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot - 20 & - \frac{1}{4} \cdot - 12 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Simplify each element in the matrix.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$X = [\begin{array}{c} \frac{- 1}{4} \cdot - 32 & - \frac{1}{4} \cdot - 20 & - \frac{1}{4} \cdot - 12 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Factor $4$ out of $- 32$ .

$X = [\begin{array}{c} \frac{- 1}{4} \cdot (4 (- 8)) & - \frac{1}{4} \cdot - 20 & - \frac{1}{4} \cdot - 12 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Cancel the common factor.

$X = [\begin{array}{c} \frac{- 1}{4} \cdot (4 \cdot - 8) & - \frac{1}{4} \cdot - 20 & - \frac{1}{4} \cdot - 12 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Rewrite the expression.

$X = [\begin{array}{c} - 1 \cdot - 8 & - \frac{1}{4} \cdot - 20 & - \frac{1}{4} \cdot - 12 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Multiply $- 1$ by $- 8$ .

$X = [\begin{array}{c} 8 & - \frac{1}{4} \cdot - 20 & - \frac{1}{4} \cdot - 12 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$X = [\begin{array}{c} 8 & \frac{- 1}{4} \cdot - 20 & - \frac{1}{4} \cdot - 12 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Factor $4$ out of $- 20$ .

$X = [\begin{array}{c} 8 & \frac{- 1}{4} \cdot (4 (- 5)) & - \frac{1}{4} \cdot - 12 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Cancel the common factor.

$X = [\begin{array}{c} 8 & \frac{- 1}{4} \cdot (4 \cdot - 5) & - \frac{1}{4} \cdot - 12 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Rewrite the expression.

$X = [\begin{array}{c} 8 & - 1 \cdot - 5 & - \frac{1}{4} \cdot - 12 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Multiply $- 1$ by $- 5$ .

$X = [\begin{array}{c} 8 & 5 & - \frac{1}{4} \cdot - 12 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$X = [\begin{array}{c} 8 & 5 & \frac{- 1}{4} \cdot - 12 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Factor $4$ out of $- 12$ .

$X = [\begin{array}{c} 8 & 5 & \frac{- 1}{4} \cdot (4 (- 3)) \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Cancel the common factor.

$X = [\begin{array}{c} 8 & 5 & \frac{- 1}{4} \cdot (4 \cdot - 3) \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Rewrite the expression.

$X = [\begin{array}{c} 8 & 5 & - 1 \cdot - 3 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Multiply $- 1$ by $- 3$ .

$X = [\begin{array}{c} 8 & 5 & 3 \\ - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$X = [\begin{array}{c} 8 & 5 & 3 \\ \frac{- 1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Factor $4$ out of $- 4$ .

$X = [\begin{array}{c} 8 & 5 & 3 \\ \frac{- 1}{4} \cdot (4 (- 1)) & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Cancel the common factor.

$X = [\begin{array}{c} 8 & 5 & 3 \\ \frac{- 1}{4} \cdot (4 \cdot - 1) & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Rewrite the expression.

$X = [\begin{array}{c} 8 & 5 & 3 \\ - 1 \cdot - 1 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Multiply $- 1$ by $- 1$ .

$X = [\begin{array}{c} 8 & 5 & 3 \\ 1 & - \frac{1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$X = [\begin{array}{c} 8 & 5 & 3 \\ 1 & \frac{- 1}{4} \cdot - 32 & - \frac{1}{4} \cdot 32 \end{array}]$

Factor $4$ out of $- 32$ .

$X = [\begin{array}{c} 8 & 5 & 3 \\ 1 & \frac{- 1}{4} \cdot (4 (- 8)) & - \frac{1}{4} \cdot 32 \end{array}]$

Cancel the common factor.

$X = [\begin{array}{c} 8 & 5 & 3 \\ 1 & \frac{- 1}{4} \cdot (4 \cdot - 8) & - \frac{1}{4} \cdot 32 \end{array}]$

Rewrite the expression.

$X = [\begin{array}{c} 8 & 5 & 3 \\ 1 & - 1 \cdot - 8 & - \frac{1}{4} \cdot 32 \end{array}]$

Multiply $- 1$ by $- 8$ .

$X = [\begin{array}{c} 8 & 5 & 3 \\ 1 & 8 & - \frac{1}{4} \cdot 32 \end{array}]$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$X = [\begin{array}{c} 8 & 5 & 3 \\ 1 & 8 & \frac{- 1}{4} \cdot 32 \end{array}]$

Factor $4$ out of $32$ .

$X = [\begin{array}{c} 8 & 5 & 3 \\ 1 & 8 & \frac{- 1}{4} \cdot (4 (8)) \end{array}]$

Cancel the common factor.

$X = [\begin{array}{c} 8 & 5 & 3 \\ 1 & 8 & \frac{- 1}{4} \cdot (4 \cdot 8) \end{array}]$

Rewrite the expression.

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

Multiply $- 1$ by $8$ .

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

Solve the Matrix Equation -4X-[[-8,-17,4],[-16,-29,17]]=[[-24,-3,-16],[12,-3,15]]

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