Linear Algebra Examples

$- \frac{9}{18} \cdot [\begin{array}{c} - 3 \\ - 3 \end{array}]$

Step 1

Cancel the common factor of $9$ and $18$ .

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Step 1.1

Factor $9$ out of $9$ .

$- \frac{9 (1)}{18} \cdot [\begin{array}{c} - 3 \\ - 3 \end{array}]$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $9$ out of $18$ .

$- \frac{9 \cdot 1}{9 \cdot 2} \cdot [\begin{array}{c} - 3 \\ - 3 \end{array}]$

Step 1.2.2

Cancel the common factor.

$- \frac{9 \cdot 1}{9 \cdot 2} \cdot [\begin{array}{c} - 3 \\ - 3 \end{array}]$

Step 1.2.3

Rewrite the expression.

$- \frac{1}{2} \cdot [\begin{array}{c} - 3 \\ - 3 \end{array}]$

Step 2

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

$[\begin{array}{c} - \frac{1}{2} \cdot - 3 \\ - \frac{1}{2} \cdot - 3 \end{array}]$

Step 3

Simplify each element in the matrix.

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Step 3.1

Multiply $- \frac{1}{2} \cdot - 3$ .

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Step 3.1.1

Multiply $- 3$ by $- 1$ .

$[\begin{array}{c} 3 (\frac{1}{2}) \\ - \frac{1}{2} \cdot - 3 \end{array}]$

Step 3.1.2

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

$[\begin{array}{c} \frac{3}{2} \\ - \frac{1}{2} \cdot - 3 \end{array}]$

Step 3.2

Multiply $- \frac{1}{2} \cdot - 3$ .

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Step 3.2.1

Multiply $- 3$ by $- 1$ .

$[\begin{array}{c} \frac{3}{2} \\ 3 (\frac{1}{2}) \end{array}]$

Step 3.2.2

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

$[\begin{array}{c} \frac{3}{2} \\ \frac{3}{2} \end{array}]$