Linear Algebra Examples

$\frac{[\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ - 2 & 3 & 1 & 0 \\ 7 & 0 & - 1 & - 3 \end{array}] \cdot 1}{2} a$

Step 1

Simplify the numerator.

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Step 1.1

Move $1$ to the left of $[\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ - 2 & 3 & 1 & 0 \\ 7 & 0 & - 1 & - 3 \end{array}]$ .

$\frac{1 \cdot [\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ - 2 & 3 & 1 & 0 \\ 7 & 0 & - 1 & - 3 \end{array}]}{2} a$

Step 1.2

Multiply $1$ by each element of the matrix.

$\frac{[\begin{array}{c} 1 \cdot 2 & 1 \cdot - 8 & 1 \cdot - 10 & 1 \cdot - 14 \\ 1 \cdot - 2 & 1 \cdot 3 & 1 \cdot 1 & 1 \cdot 0 \\ 1 \cdot 7 & 1 \cdot 0 & 1 \cdot - 1 & 1 \cdot - 3 \end{array}]}{2} a$

Step 1.3

Simplify each element in the matrix.

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Step 1.3.1

Multiply $2$ by $1$ .

$\frac{[\begin{array}{c} 2 & 1 \cdot - 8 & 1 \cdot - 10 & 1 \cdot - 14 \\ 1 \cdot - 2 & 1 \cdot 3 & 1 \cdot 1 & 1 \cdot 0 \\ 1 \cdot 7 & 1 \cdot 0 & 1 \cdot - 1 & 1 \cdot - 3 \end{array}]}{2} a$

Step 1.3.2

Multiply $- 8$ by $1$ .

$\frac{[\begin{array}{c} 2 & - 8 & 1 \cdot - 10 & 1 \cdot - 14 \\ 1 \cdot - 2 & 1 \cdot 3 & 1 \cdot 1 & 1 \cdot 0 \\ 1 \cdot 7 & 1 \cdot 0 & 1 \cdot - 1 & 1 \cdot - 3 \end{array}]}{2} a$

Step 1.3.3

Multiply $- 10$ by $1$ .

$\frac{[\begin{array}{c} 2 & - 8 & - 10 & 1 \cdot - 14 \\ 1 \cdot - 2 & 1 \cdot 3 & 1 \cdot 1 & 1 \cdot 0 \\ 1 \cdot 7 & 1 \cdot 0 & 1 \cdot - 1 & 1 \cdot - 3 \end{array}]}{2} a$

Step 1.3.4

Multiply $- 14$ by $1$ .

$\frac{[\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ 1 \cdot - 2 & 1 \cdot 3 & 1 \cdot 1 & 1 \cdot 0 \\ 1 \cdot 7 & 1 \cdot 0 & 1 \cdot - 1 & 1 \cdot - 3 \end{array}]}{2} a$

Step 1.3.5

Multiply $- 2$ by $1$ .

$\frac{[\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ - 2 & 1 \cdot 3 & 1 \cdot 1 & 1 \cdot 0 \\ 1 \cdot 7 & 1 \cdot 0 & 1 \cdot - 1 & 1 \cdot - 3 \end{array}]}{2} a$

Step 1.3.6

Multiply $3$ by $1$ .

$\frac{[\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ - 2 & 3 & 1 \cdot 1 & 1 \cdot 0 \\ 1 \cdot 7 & 1 \cdot 0 & 1 \cdot - 1 & 1 \cdot - 3 \end{array}]}{2} a$

Step 1.3.7

Multiply $1$ by $1$ .

$\frac{[\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ - 2 & 3 & 1 & 1 \cdot 0 \\ 1 \cdot 7 & 1 \cdot 0 & 1 \cdot - 1 & 1 \cdot - 3 \end{array}]}{2} a$

Step 1.3.8

Multiply $0$ by $1$ .

$\frac{[\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ - 2 & 3 & 1 & 0 \\ 1 \cdot 7 & 1 \cdot 0 & 1 \cdot - 1 & 1 \cdot - 3 \end{array}]}{2} a$

Step 1.3.9

Multiply $7$ by $1$ .

$\frac{[\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ - 2 & 3 & 1 & 0 \\ 7 & 1 \cdot 0 & 1 \cdot - 1 & 1 \cdot - 3 \end{array}]}{2} a$

Step 1.3.10

Multiply $0$ by $1$ .

$\frac{[\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ - 2 & 3 & 1 & 0 \\ 7 & 0 & 1 \cdot - 1 & 1 \cdot - 3 \end{array}]}{2} a$

Step 1.3.11

Multiply $- 1$ by $1$ .

$\frac{[\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ - 2 & 3 & 1 & 0 \\ 7 & 0 & - 1 & 1 \cdot - 3 \end{array}]}{2} a$

Step 1.3.12

Multiply $- 3$ by $1$ .

$\frac{[\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ - 2 & 3 & 1 & 0 \\ 7 & 0 & - 1 & - 3 \end{array}]}{2} a$

Step 2

Reorder factors in $\frac{[\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ - 2 & 3 & 1 & 0 \\ 7 & 0 & - 1 & - 3 \end{array}]}{2} a$ .

$a \frac{[\begin{array}{c} 2 & - 8 & - 10 & - 14 \\ - 2 & 3 & 1 & 0 \\ 7 & 0 & - 1 & - 3 \end{array}]}{2}$