Lineare Algebra Beispiele

$3 [\begin{array}{c} 0 & 0 & 2 \\ 3 & 1 & 0 \\ 0 & - 2 & 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 1

Multipliziere $3$ mit jedem Element der Matrix.

$[\begin{array}{c} 3 \cdot 0 & 3 \cdot 0 & 3 \cdot 2 \\ 3 \cdot 3 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 2

Vereinfache jedes Element der Matrix.

Tippen, um mehr Schritte zu sehen ...

Stelle $3 \cdot 0$ um.

$[\begin{array}{c} 0 & 3 \cdot 0 & 3 \cdot 2 \\ 3 \cdot 3 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $3 \cdot 0$ um.

$[\begin{array}{c} 0 & 0 & 3 \cdot 2 \\ 3 \cdot 3 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $3 \cdot 2$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 3 \cdot 3 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $3 \cdot 3$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $3 \cdot 1$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $3 \cdot 0$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $3 \cdot 0$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $3 \cdot - 2$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $3 \cdot 4$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 3

Multipliziere $- 2$ mit jedem Element der Matrix.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} - 2 \cdot 0 & - 2 \cdot 2 & - 2 \cdot 1 \\ - 2 \cdot 3 & - 2 \cdot 0 & - 2 \cdot 5 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 4

Vereinfache jedes Element der Matrix.

Tippen, um mehr Schritte zu sehen ...

Stelle $- 2 \cdot 0$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 2 \cdot 2 & - 2 \cdot 1 \\ - 2 \cdot 3 & - 2 \cdot 0 & - 2 \cdot 5 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $- 2 \cdot 2$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \cdot 1 \\ - 2 \cdot 3 & - 2 \cdot 0 & - 2 \cdot 5 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $- 2 \cdot 1$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 2 \cdot 3 & - 2 \cdot 0 & - 2 \cdot 5 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $- 2 \cdot 3$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & - 2 \cdot 0 & - 2 \cdot 5 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $- 2 \cdot 0$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 2 \cdot 5 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $- 2 \cdot 5$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $- 2 \cdot 7$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $- 2 \cdot - 6$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $- 2 \cdot 0$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 5

Multipliziere $8$ mit jedem Element der Matrix.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 \cdot 1 & 8 \cdot - 1 & 8 \cdot 2 \\ 8 \cdot 3 & 8 \cdot 4 & 8 \cdot 5 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 6

Vereinfache jedes Element der Matrix.

Tippen, um mehr Schritte zu sehen ...

Stelle $8 \cdot 1$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & 8 \cdot - 1 & 8 \cdot 2 \\ 8 \cdot 3 & 8 \cdot 4 & 8 \cdot 5 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $8 \cdot - 1$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 8 \cdot 2 \\ 8 \cdot 3 & 8 \cdot 4 & 8 \cdot 5 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $8 \cdot 2$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 8 \cdot 3 & 8 \cdot 4 & 8 \cdot 5 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $8 \cdot 3$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 8 \cdot 4 & 8 \cdot 5 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $8 \cdot 4$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 8 \cdot 5 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $8 \cdot 5$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $8 \cdot 0$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $8 \cdot 1$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Stelle $8 \cdot - 1$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 7

Multipliziere $- 4$ mit jedem Element der Matrix.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} - 4 \cdot 0 & - 4 \cdot 25 & - 4 \cdot 12 & - 4 \cdot 5 \\ - 4 \cdot 6 & - 4 \cdot 75 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Step 8

Vereinfache jedes Element der Matrix.

Tippen, um mehr Schritte zu sehen ...

Stelle $- 4 \cdot 0$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 4 \cdot 25 & - 4 \cdot 12 & - 4 \cdot 5 \\ - 4 \cdot 6 & - 4 \cdot 75 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Stelle $- 4 \cdot 25$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 4 \cdot 12 & - 4 \cdot 5 \\ - 4 \cdot 6 & - 4 \cdot 75 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Stelle $- 4 \cdot 12$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 4 \cdot 5 \\ - 4 \cdot 6 & - 4 \cdot 75 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Stelle $- 4 \cdot 5$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 4 \cdot 6 & - 4 \cdot 75 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Stelle $- 4 \cdot 6$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 4 \cdot 75 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Stelle $- 4 \cdot 75$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Stelle $- 4 \cdot 8$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Stelle $- 4 \cdot 75$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Stelle $- 4 \cdot 7$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Stelle $- 4 \cdot 5$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Stelle $- 4 \cdot - 3$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Stelle $- 4 \cdot 5$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Stelle $- 4 \cdot 3.5$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & - 4 \cdot - 1 \end{array}]$

Stelle $- 4 \cdot - 1$ um.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Step 9

Addiere die entsprechenden Elemente.

$[\begin{array}{c} 0 + 0 & 0 - 4 & 6 - 2 \\ 9 - 6 & 3 + 0 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Step 10

Vereinfache jedes Element der Matrix $[\begin{array}{c} 0 + 0 & 0 - 4 & 6 - 2 \\ 9 - 6 & 3 + 0 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}]$ .

Tippen, um mehr Schritte zu sehen ...

Vereinfache $0 + 0$ .

$[\begin{array}{c} 0 & 0 - 4 & 6 - 2 \\ 9 - 6 & 3 + 0 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $0 - 4$ .

$[\begin{array}{c} 0 & - 4 & 6 - 2 \\ 9 - 6 & 3 + 0 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $6 - 2$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 9 - 6 & 3 + 0 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $9 - 6$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 3 & 3 + 0 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $3 + 0$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 3 & 3 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $0 - 10$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 3 & 3 & - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $0 - 14$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 3 & 3 & - 10 \\ - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $- 6 + 12$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 3 & 3 & - 10 \\ - 14 & 6 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $12 + 0$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 3 & 3 & - 10 \\ - 14 & 6 & 12 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Step 11

Addiere die entsprechenden Elemente.

$[\begin{array}{c} 0 + 8 & - 4 - 8 & 4 + 16 \\ 3 + 24 & 3 + 32 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Step 12

Vereinfache jedes Element der Matrix $[\begin{array}{c} 0 + 8 & - 4 - 8 & 4 + 16 \\ 3 + 24 & 3 + 32 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}]$ .

Tippen, um mehr Schritte zu sehen ...

Vereinfache $0 + 8$ .

$[\begin{array}{c} 8 & - 4 - 8 & 4 + 16 \\ 3 + 24 & 3 + 32 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $- 4 - 8$ .

$[\begin{array}{c} 8 & - 12 & 4 + 16 \\ 3 + 24 & 3 + 32 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $4 + 16$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 3 + 24 & 3 + 32 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $3 + 24$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 27 & 3 + 32 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $3 + 32$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 27 & 35 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $- 10 + 40$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 27 & 35 & 30 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $- 14 + 0$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 27 & 35 & 30 \\ - 14 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $6 + 8$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 27 & 35 & 30 \\ - 14 & 14 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Vereinfache $12 - 8$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 27 & 35 & 30 \\ - 14 & 14 & 4 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$