Algebra Examples

$\frac{7}{2} [\begin{array}{c} - 14 & 4 \\ 4 & 0 \end{array}]$

Step 1

Multiply $\frac{7}{2}$ by each element of the matrix.

$[\begin{array}{c} \frac{7}{2} \cdot - 14 & \frac{7}{2} \cdot 4 \\ \frac{7}{2} \cdot 4 & \frac{7}{2} \cdot 0 \end{array}]$

Step 2

Simplify each element in the matrix.

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Step 2.1

Cancel the common factor of $2$ .

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Step 2.1.1

Factor $2$ out of $- 14$ .

$[\begin{array}{c} \frac{7}{2} \cdot (2 (- 7)) & \frac{7}{2} \cdot 4 \\ \frac{7}{2} \cdot 4 & \frac{7}{2} \cdot 0 \end{array}]$

Step 2.1.2

Cancel the common factor.

$[\begin{array}{c} \frac{7}{2} \cdot (2 \cdot - 7) & \frac{7}{2} \cdot 4 \\ \frac{7}{2} \cdot 4 & \frac{7}{2} \cdot 0 \end{array}]$

Step 2.1.3

Rewrite the expression.

$[\begin{array}{c} 7 \cdot - 7 & \frac{7}{2} \cdot 4 \\ \frac{7}{2} \cdot 4 & \frac{7}{2} \cdot 0 \end{array}]$

Step 2.2

Multiply $7$ by $- 7$ .

$[\begin{array}{c} - 49 & \frac{7}{2} \cdot 4 \\ \frac{7}{2} \cdot 4 & \frac{7}{2} \cdot 0 \end{array}]$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $4$ .

$[\begin{array}{c} - 49 & \frac{7}{2} \cdot (2 (2)) \\ \frac{7}{2} \cdot 4 & \frac{7}{2} \cdot 0 \end{array}]$

Step 2.3.2

Cancel the common factor.

$[\begin{array}{c} - 49 & \frac{7}{2} \cdot (2 \cdot 2) \\ \frac{7}{2} \cdot 4 & \frac{7}{2} \cdot 0 \end{array}]$

Step 2.3.3

Rewrite the expression.

$[\begin{array}{c} - 49 & 7 \cdot 2 \\ \frac{7}{2} \cdot 4 & \frac{7}{2} \cdot 0 \end{array}]$

Step 2.4

Multiply $7$ by $2$ .

$[\begin{array}{c} - 49 & 14 \\ \frac{7}{2} \cdot 4 & \frac{7}{2} \cdot 0 \end{array}]$

Step 2.5

Cancel the common factor of $2$ .

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Step 2.5.1

Factor $2$ out of $4$ .

$[\begin{array}{c} - 49 & 14 \\ \frac{7}{2} \cdot (2 (2)) & \frac{7}{2} \cdot 0 \end{array}]$

Step 2.5.2

Cancel the common factor.

$[\begin{array}{c} - 49 & 14 \\ \frac{7}{2} \cdot (2 \cdot 2) & \frac{7}{2} \cdot 0 \end{array}]$

Step 2.5.3

Rewrite the expression.

$[\begin{array}{c} - 49 & 14 \\ 7 \cdot 2 & \frac{7}{2} \cdot 0 \end{array}]$

Step 2.6

Multiply $7$ by $2$ .

$[\begin{array}{c} - 49 & 14 \\ 14 & \frac{7}{2} \cdot 0 \end{array}]$

Step 2.7

Multiply $\frac{7}{2}$ by $0$ .

$[\begin{array}{c} - 49 & 14 \\ 14 & 0 \end{array}]$