Precalculus Examples

$2 X - [\begin{array}{c} - 4 & 9 & 10 \\ 1 & 16 & 2 \end{array}] = [\begin{array}{c} - 22 & - 7 & - 1 \\ - 4 & - 28 & - 18 \end{array}]$

Step 1

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

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Step 1.1

Add $[\begin{array}{c} - 4 & 9 & 10 \\ 1 & 16 & 2 \end{array}]$ to both sides of the equation.

$2 X = [\begin{array}{c} - 22 & - 7 & - 1 \\ - 4 & - 28 & - 18 \end{array}] + [\begin{array}{c} - 4 & 9 & 10 \\ 1 & 16 & 2 \end{array}]$

Step 2

Simplify the right side.

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Step 2.1

Add the corresponding elements.

$2 X = [\begin{array}{c} - 22 - 4 & - 7 + 9 & - 1 + 10 \\ - 4 + 1 & - 28 + 16 & - 18 + 2 \end{array}]$

Step 2.2

Simplify each element.

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Step 2.2.1

Subtract $4$ from $- 22$ .

$2 X = [\begin{array}{c} - 26 & - 7 + 9 & - 1 + 10 \\ - 4 + 1 & - 28 + 16 & - 18 + 2 \end{array}]$

Step 2.2.2

Add $- 7$ and $9$ .

$2 X = [\begin{array}{c} - 26 & 2 & - 1 + 10 \\ - 4 + 1 & - 28 + 16 & - 18 + 2 \end{array}]$

Step 2.2.3

Add $- 1$ and $10$ .

$2 X = [\begin{array}{c} - 26 & 2 & 9 \\ - 4 + 1 & - 28 + 16 & - 18 + 2 \end{array}]$

Step 2.2.4

Add $- 4$ and $1$ .

$2 X = [\begin{array}{c} - 26 & 2 & 9 \\ - 3 & - 28 + 16 & - 18 + 2 \end{array}]$

Step 2.2.5

Add $- 28$ and $16$ .

$2 X = [\begin{array}{c} - 26 & 2 & 9 \\ - 3 & - 12 & - 18 + 2 \end{array}]$

Step 2.2.6

Add $- 18$ and $2$ .

$2 X = [\begin{array}{c} - 26 & 2 & 9 \\ - 3 & - 12 & - 16 \end{array}]$

Step 3

Multiply both sides by $\frac{1}{2}$ .

$\frac{1}{2} (2 X) = \frac{1}{2} [\begin{array}{c} - 26 & 2 & 9 \\ - 3 & - 12 & - 16 \end{array}]$

Step 4

Simplify.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Factor $2$ out of $2 X$ .

$\frac{1}{2} (2 (X)) = \frac{1}{2} [\begin{array}{c} - 26 & 2 & 9 \\ - 3 & - 12 & - 16 \end{array}]$

Step 4.1.2

Cancel the common factor.

$\frac{1}{2} (2 X) = \frac{1}{2} [\begin{array}{c} - 26 & 2 & 9 \\ - 3 & - 12 & - 16 \end{array}]$

Step 4.1.3

Rewrite the expression.

$X = \frac{1}{2} [\begin{array}{c} - 26 & 2 & 9 \\ - 3 & - 12 & - 16 \end{array}]$

Step 4.2

Multiply $\frac{1}{2}$ by each element of the matrix.

$X = [\begin{array}{c} \frac{1}{2} \cdot - 26 & \frac{1}{2} \cdot 2 & \frac{1}{2} \cdot 9 \\ \frac{1}{2} \cdot - 3 & \frac{1}{2} \cdot - 12 & \frac{1}{2} \cdot - 16 \end{array}]$

Step 4.3

Simplify each element in the matrix.

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Step 4.3.1

Cancel the common factor of $2$ .

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Step 4.3.1.1

Factor $2$ out of $- 26$ .

$X = [\begin{array}{c} \frac{1}{2} \cdot (2 (- 13)) & \frac{1}{2} \cdot 2 & \frac{1}{2} \cdot 9 \\ \frac{1}{2} \cdot - 3 & \frac{1}{2} \cdot - 12 & \frac{1}{2} \cdot - 16 \end{array}]$

Step 4.3.1.2

Cancel the common factor.

$X = [\begin{array}{c} \frac{1}{2} \cdot (2 \cdot - 13) & \frac{1}{2} \cdot 2 & \frac{1}{2} \cdot 9 \\ \frac{1}{2} \cdot - 3 & \frac{1}{2} \cdot - 12 & \frac{1}{2} \cdot - 16 \end{array}]$

Step 4.3.1.3

Rewrite the expression.

$X = [\begin{array}{c} - 13 & \frac{1}{2} \cdot 2 & \frac{1}{2} \cdot 9 \\ \frac{1}{2} \cdot - 3 & \frac{1}{2} \cdot - 12 & \frac{1}{2} \cdot - 16 \end{array}]$

Step 4.3.2

Cancel the common factor of $2$ .

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Step 4.3.2.1

Cancel the common factor.

$X = [\begin{array}{c} - 13 & \frac{1}{2} \cdot 2 & \frac{1}{2} \cdot 9 \\ \frac{1}{2} \cdot - 3 & \frac{1}{2} \cdot - 12 & \frac{1}{2} \cdot - 16 \end{array}]$

Step 4.3.2.2

Rewrite the expression.

$X = [\begin{array}{c} - 13 & 1 & \frac{1}{2} \cdot 9 \\ \frac{1}{2} \cdot - 3 & \frac{1}{2} \cdot - 12 & \frac{1}{2} \cdot - 16 \end{array}]$

Step 4.3.3

Combine $\frac{1}{2}$ and $9$ .

$X = [\begin{array}{c} - 13 & 1 & \frac{9}{2} \\ \frac{1}{2} \cdot - 3 & \frac{1}{2} \cdot - 12 & \frac{1}{2} \cdot - 16 \end{array}]$

Step 4.3.4

Combine $\frac{1}{2}$ and $- 3$ .

$X = [\begin{array}{c} - 13 & 1 & \frac{9}{2} \\ \frac{- 3}{2} & \frac{1}{2} \cdot - 12 & \frac{1}{2} \cdot - 16 \end{array}]$

Step 4.3.5

Move the negative in front of the fraction.

$X = [\begin{array}{c} - 13 & 1 & \frac{9}{2} \\ - \frac{3}{2} & \frac{1}{2} \cdot - 12 & \frac{1}{2} \cdot - 16 \end{array}]$

Step 4.3.6

Cancel the common factor of $2$ .

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Step 4.3.6.1

Factor $2$ out of $- 12$ .

$X = [\begin{array}{c} - 13 & 1 & \frac{9}{2} \\ - \frac{3}{2} & \frac{1}{2} \cdot (2 (- 6)) & \frac{1}{2} \cdot - 16 \end{array}]$

Step 4.3.6.2

Cancel the common factor.

$X = [\begin{array}{c} - 13 & 1 & \frac{9}{2} \\ - \frac{3}{2} & \frac{1}{2} \cdot (2 \cdot - 6) & \frac{1}{2} \cdot - 16 \end{array}]$

Step 4.3.6.3

Rewrite the expression.

$X = [\begin{array}{c} - 13 & 1 & \frac{9}{2} \\ - \frac{3}{2} & - 6 & \frac{1}{2} \cdot - 16 \end{array}]$

Step 4.3.7

Cancel the common factor of $2$ .

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Step 4.3.7.1

Factor $2$ out of $- 16$ .

$X = [\begin{array}{c} - 13 & 1 & \frac{9}{2} \\ - \frac{3}{2} & - 6 & \frac{1}{2} \cdot (2 (- 8)) \end{array}]$

Step 4.3.7.2

Cancel the common factor.

$X = [\begin{array}{c} - 13 & 1 & \frac{9}{2} \\ - \frac{3}{2} & - 6 & \frac{1}{2} \cdot (2 \cdot - 8) \end{array}]$

Step 4.3.7.3

Rewrite the expression.

$X = [\begin{array}{c} - 13 & 1 & \frac{9}{2} \\ - \frac{3}{2} & - 6 & - 8 \end{array}]$