Linear Algebra Examples

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - \frac{21}{3} \\ - \frac{9}{3} & 2 & - \frac{18}{3} & - \frac{33}{3} & - \frac{18}{3} & 0 \\ - \frac{21}{3} & - \frac{3}{3} & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 1

Divide $21$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 1 \cdot 7 \\ - \frac{9}{3} & 2 & - \frac{18}{3} & - \frac{33}{3} & - \frac{18}{3} & 0 \\ - \frac{21}{3} & - \frac{3}{3} & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 2

Multiply $- 1$ by $7$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - \frac{9}{3} & 2 & - \frac{18}{3} & - \frac{33}{3} & - \frac{18}{3} & 0 \\ - \frac{21}{3} & - \frac{3}{3} & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 3

Divide $9$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 1 \cdot 3 & 2 & - \frac{18}{3} & - \frac{33}{3} & - \frac{18}{3} & 0 \\ - \frac{21}{3} & - \frac{3}{3} & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 4

Multiply $- 1$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - \frac{18}{3} & - \frac{33}{3} & - \frac{18}{3} & 0 \\ - \frac{21}{3} & - \frac{3}{3} & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 5

Divide $18$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 1 \cdot 6 & - \frac{33}{3} & - \frac{18}{3} & 0 \\ - \frac{21}{3} & - \frac{3}{3} & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 6

Multiply $- 1$ by $6$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - \frac{33}{3} & - \frac{18}{3} & 0 \\ - \frac{21}{3} & - \frac{3}{3} & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 7

Divide $33$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 1 \cdot 11 & - \frac{18}{3} & 0 \\ - \frac{21}{3} & - \frac{3}{3} & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 8

Multiply $- 1$ by $11$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - \frac{18}{3} & 0 \\ - \frac{21}{3} & - \frac{3}{3} & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 9

Divide $18$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 1 \cdot 6 & 0 \\ - \frac{21}{3} & - \frac{3}{3} & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 10

Multiply $- 1$ by $6$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - \frac{21}{3} & - \frac{3}{3} & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 11

Divide $21$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 1 \cdot 7 & - \frac{3}{3} & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 12

Multiply $- 1$ by $7$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - \frac{3}{3} & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 13

Cancel the common factor of $3$ .

Tap for more steps...

Step 13.1

Cancel the common factor.

Step 13.2

Rewrite the expression.

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 \cdot 1 & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 14

Multiply $- 1$ by $1$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & \frac{15}{3} & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 15

Divide $15$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - \frac{15}{3} & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 16

Divide $15$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 1 \cdot 5 & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 17

Multiply $- 1$ by $5$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & \frac{39}{3} & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 18

Divide $39$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & 13 & - \frac{12}{3} \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 19

Divide $12$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & 13 & - 1 \cdot 4 \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 20

Multiply $- 1$ by $4$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & 13 & - 4 \\ \frac{3}{3} & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 21

Divide $3$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & 13 & - 4 \\ 1 & - \frac{15}{3} & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 22

Divide $15$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & 13 & - 4 \\ 1 & - 1 \cdot 5 & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 23

Multiply $- 1$ by $5$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & 13 & - 4 \\ 1 & - 5 & - \frac{27}{3} & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 24

Divide $27$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & 13 & - 4 \\ 1 & - 5 & - 1 \cdot 9 & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 25

Multiply $- 1$ by $9$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & 13 & - 4 \\ 1 & - 5 & - 9 & \frac{18}{3} & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 26

Divide $18$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & 13 & - 4 \\ 1 & - 5 & - 9 & 6 & - \frac{3}{3} & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 27

Cancel the common factor of $3$ .

Tap for more steps...

Step 27.1

Cancel the common factor.

Step 27.2

Rewrite the expression.

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & 13 & - 4 \\ 1 & - 5 & - 9 & 6 & - 1 \cdot 1 & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 28

Multiply $- 1$ by $1$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & 13 & - 4 \\ 1 & - 5 & - 9 & 6 & - 1 & \frac{15}{3} \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 29

Divide $15$ by $3$ .

$[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & 13 & - 4 \\ 1 & - 5 & - 9 & 6 & - 1 & 5 \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$

Step 30

Multiply $[\begin{array}{c} - 6 & - 1 & - 3 & - 6 & - 1 & 9 \\ 2 & - 1 & 4 & 3 & - 7 & 1 \\ 0 & 2 & - 7 & - 9 & 6 & - 7 \\ - 3 & 2 & - 6 & - 11 & - 6 & 0 \\ - 7 & - 1 & 5 & - 5 & 13 & - 4 \\ 1 & - 5 & - 9 & 6 & - 1 & 5 \end{array}] [\begin{array}{c} - 1 & 2 & - 1 & 1 & - 1 & 2 \\ - 7 & 2 & - 7 & 0 & - 2 & 5 \\ 3 & 3 & - 3 & 0 & - 1 & 7 \\ 7 & 2 & 7 & - 3 & 0 & - 3 \\ 3 & - 1 & 4 & 5 & 2 & - 4 \\ - 2 & - 9 & 12 & 2 & 0 & 2 \end{array}]$ .

Tap for more steps...

Step 30.1

Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is $6 \times 6$ and the second matrix is $6 \times 6$ .

Step 30.2

Multiply each row in the first matrix by each column in the second matrix.

$[\begin{array}{c} - 6 \cdot - 1 - - 7 - 3 \cdot 3 - 6 \cdot 7 - 1 \cdot 3 + 9 \cdot - 2 & - 6 \cdot 2 - 1 \cdot 2 - 3 \cdot 3 - 6 \cdot 2 - - 1 + 9 \cdot - 9 & - 6 \cdot - 1 - - 7 - 3 \cdot - 3 - 6 \cdot 7 - 1 \cdot 4 + 9 \cdot 12 & - 6 \cdot 1 - 0 - 3 \cdot 0 - 6 \cdot - 3 - 1 \cdot 5 + 9 \cdot 2 & - 6 \cdot - 1 - - 2 - 3 \cdot - 1 - 6 \cdot 0 - 1 \cdot 2 + 9 \cdot 0 & - 6 \cdot 2 - 1 \cdot 5 - 3 \cdot 7 - 6 \cdot - 3 - - 4 + 9 \cdot 2 \\ 2 \cdot - 1 - - 7 + 4 \cdot 3 + 3 \cdot 7 - 7 \cdot 3 + 1 \cdot - 2 & 2 \cdot 2 - 1 \cdot 2 + 4 \cdot 3 + 3 \cdot 2 - 7 \cdot - 1 + 1 \cdot - 9 & 2 \cdot - 1 - - 7 + 4 \cdot - 3 + 3 \cdot 7 - 7 \cdot 4 + 1 \cdot 12 & 2 \cdot 1 - 0 + 4 \cdot 0 + 3 \cdot - 3 - 7 \cdot 5 + 1 \cdot 2 & 2 \cdot - 1 - - 2 + 4 \cdot - 1 + 3 \cdot 0 - 7 \cdot 2 + 1 \cdot 0 & 2 \cdot 2 - 1 \cdot 5 + 4 \cdot 7 + 3 \cdot - 3 - 7 \cdot - 4 + 1 \cdot 2 \\ 0 \cdot - 1 + 2 \cdot - 7 - 7 \cdot 3 - 9 \cdot 7 + 6 \cdot 3 - 7 \cdot - 2 & 0 \cdot 2 + 2 \cdot 2 - 7 \cdot 3 - 9 \cdot 2 + 6 \cdot - 1 - 7 \cdot - 9 & 0 \cdot - 1 + 2 \cdot - 7 - 7 \cdot - 3 - 9 \cdot 7 + 6 \cdot 4 - 7 \cdot 12 & 0 \cdot 1 + 2 \cdot 0 - 7 \cdot 0 - 9 \cdot - 3 + 6 \cdot 5 - 7 \cdot 2 & 0 \cdot - 1 + 2 \cdot - 2 - 7 \cdot - 1 - 9 \cdot 0 + 6 \cdot 2 - 7 \cdot 0 & 0 \cdot 2 + 2 \cdot 5 - 7 \cdot 7 - 9 \cdot - 3 + 6 \cdot - 4 - 7 \cdot 2 \\ - 3 \cdot - 1 + 2 \cdot - 7 - 6 \cdot 3 - 11 \cdot 7 - 6 \cdot 3 + 0 \cdot - 2 & - 3 \cdot 2 + 2 \cdot 2 - 6 \cdot 3 - 11 \cdot 2 - 6 \cdot - 1 + 0 \cdot - 9 & - 3 \cdot - 1 + 2 \cdot - 7 - 6 \cdot - 3 - 11 \cdot 7 - 6 \cdot 4 + 0 \cdot 12 & - 3 \cdot 1 + 2 \cdot 0 - 6 \cdot 0 - 11 \cdot - 3 - 6 \cdot 5 + 0 \cdot 2 & - 3 \cdot - 1 + 2 \cdot - 2 - 6 \cdot - 1 - 11 \cdot 0 - 6 \cdot 2 + 0 \cdot 0 & - 3 \cdot 2 + 2 \cdot 5 - 6 \cdot 7 - 11 \cdot - 3 - 6 \cdot - 4 + 0 \cdot 2 \\ - 7 \cdot - 1 - - 7 + 5 \cdot 3 - 5 \cdot 7 + 13 \cdot 3 - 4 \cdot - 2 & - 7 \cdot 2 - 1 \cdot 2 + 5 \cdot 3 - 5 \cdot 2 + 13 \cdot - 1 - 4 \cdot - 9 & - 7 \cdot - 1 - - 7 + 5 \cdot - 3 - 5 \cdot 7 + 13 \cdot 4 - 4 \cdot 12 & - 7 \cdot 1 - 0 + 5 \cdot 0 - 5 \cdot - 3 + 13 \cdot 5 - 4 \cdot 2 & - 7 \cdot - 1 - - 2 + 5 \cdot - 1 - 5 \cdot 0 + 13 \cdot 2 - 4 \cdot 0 & - 7 \cdot 2 - 1 \cdot 5 + 5 \cdot 7 - 5 \cdot - 3 + 13 \cdot - 4 - 4 \cdot 2 \\ 1 \cdot - 1 - 5 \cdot - 7 - 9 \cdot 3 + 6 \cdot 7 - 1 \cdot 3 + 5 \cdot - 2 & 1 \cdot 2 - 5 \cdot 2 - 9 \cdot 3 + 6 \cdot 2 - - 1 + 5 \cdot - 9 & 1 \cdot - 1 - 5 \cdot - 7 - 9 \cdot - 3 + 6 \cdot 7 - 1 \cdot 4 + 5 \cdot 12 & 1 \cdot 1 - 5 \cdot 0 - 9 \cdot 0 + 6 \cdot - 3 - 1 \cdot 5 + 5 \cdot 2 & 1 \cdot - 1 - 5 \cdot - 2 - 9 \cdot - 1 + 6 \cdot 0 - 1 \cdot 2 + 5 \cdot 0 & 1 \cdot 2 - 5 \cdot 5 - 9 \cdot 7 + 6 \cdot - 3 - - 4 + 5 \cdot 2 \end{array}]$

Step 30.3

Simplify each element of the matrix by multiplying out all the expressions.

$[\begin{array}{c} - 59 & - 115 & 84 & 25 & 9 & 2 \\ 15 & 18 & - 2 & - 40 & - 18 & 48 \\ - 66 & 22 & - 116 & 43 & 15 & - 50 \\ - 124 & - 36 & - 94 & 0 & - 7 & 19 \\ 41 & 12 & - 32 & 65 & 30 & - 29 \\ 36 & - 67 & 159 & - 12 & 16 & - 90 \end{array}]$