Lineare Algebra Beispiele

$[\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}] + [\begin{array}{c} 0 & - 1 & 0 & - 2 \\ - 1 & 1 & 2 & - 2 \\ 0 & - 1 & - 3 & 3 \\ 2 & - 2 & - 3 & 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 1

Addiere die entsprechenden Elemente.

$[\begin{array}{c} 0 + 0 & 1 - 1 & 0 + 0 & 2 - 2 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2

Simplify each element.

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Schritt 2.1

Addiere $0$ und $0$ .

$[\begin{array}{c} 0 & 1 - 1 & 0 + 0 & 2 - 2 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.2

Subtrahiere $1$ von $1$ .

$[\begin{array}{c} 0 & 0 & 0 + 0 & 2 - 2 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.3

Addiere $0$ und $0$ .

$[\begin{array}{c} 0 & 0 & 0 & 2 - 2 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.4

Subtrahiere $2$ von $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 1 - 1 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.5

Subtrahiere $1$ von $1$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & - 1 + 1 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.6

Addiere $- 1$ und $1$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & - 2 + 2 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.7

Addiere $- 2$ und $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 2 - 2 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.8

Subtrahiere $2$ von $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 + 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.9

Addiere $0$ und $0$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 1 - 1 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.10

Subtrahiere $1$ von $1$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 3 - 3 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.11

Subtrahiere $3$ von $3$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & - 3 + 3 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.12

Addiere $- 3$ und $3$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ - 2 + 2 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.13

Addiere $- 2$ und $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 2 - 2 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.14

Subtrahiere $2$ von $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 3 - 3 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.15

Subtrahiere $3$ von $3$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & - 2 + 2 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 2.16

Addiere $- 2$ und $2$ .

$[\begin{array}{c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3

Adding any matrix to a null matrix is the matrix itself.

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Schritt 3.1

Addiere die entsprechenden Elemente.

$[\begin{array}{c} 0 + 1 & 0 + 3 & 0 - 2 & 0 - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2

Simplify each element.

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Schritt 3.2.1

Addiere $0$ und $1$ .

$[\begin{array}{c} 1 & 0 + 3 & 0 - 2 & 0 - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.2

Addiere $0$ und $3$ .

$[\begin{array}{c} 1 & 3 & 0 - 2 & 0 - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.3

Subtrahiere $2$ von $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & 0 - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.4

Subtrahiere $1$ von $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ 0 - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.5

Subtrahiere $3$ von $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & 0 - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.6

Subtrahiere $12$ von $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 0 + 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.7

Addiere $0$ und $10$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 0 + 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.8

Addiere $0$ und $6$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 + 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.9

Addiere $0$ und $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & 0 - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.10

Subtrahiere $2$ von $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 0 + 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.11

Addiere $0$ und $2$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 0 + 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.12

Addiere $0$ und $1$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ 0 - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.13

Subtrahiere $2$ von $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & 0 - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.14

Subtrahiere $6$ von $0$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 0 + 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.15

Addiere $0$ und $5$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 0 + 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 3.2.16

Addiere $0$ und $3$ .

$[\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 1 & 3 & - 2 & - 1 \\ - 3 & - 12 & 10 & 6 \\ 0 & - 2 & 2 & 1 \\ - 2 & - 6 & 5 & 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 4

Addiere die entsprechenden Elemente.

$[\begin{array}{c} 1 + 1 & 3 + 3 & - 2 - 2 & - 1 - 1 \\ - 3 - 3 & - 12 - 12 & 10 + 10 & 6 + 6 \\ 0 + 0 & - 2 - 2 & 2 + 2 & 1 + 1 \\ - 2 - 2 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5

Simplify each element.

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Schritt 5.1

Addiere $1$ und $1$ .

$[\begin{array}{c} 2 & 3 + 3 & - 2 - 2 & - 1 - 1 \\ - 3 - 3 & - 12 - 12 & 10 + 10 & 6 + 6 \\ 0 + 0 & - 2 - 2 & 2 + 2 & 1 + 1 \\ - 2 - 2 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.2

Addiere $3$ und $3$ .

$[\begin{array}{c} 2 & 6 & - 2 - 2 & - 1 - 1 \\ - 3 - 3 & - 12 - 12 & 10 + 10 & 6 + 6 \\ 0 + 0 & - 2 - 2 & 2 + 2 & 1 + 1 \\ - 2 - 2 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.3

Subtrahiere $2$ von $- 2$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 1 - 1 \\ - 3 - 3 & - 12 - 12 & 10 + 10 & 6 + 6 \\ 0 + 0 & - 2 - 2 & 2 + 2 & 1 + 1 \\ - 2 - 2 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.4

Subtrahiere $1$ von $- 1$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 2 \\ - 3 - 3 & - 12 - 12 & 10 + 10 & 6 + 6 \\ 0 + 0 & - 2 - 2 & 2 + 2 & 1 + 1 \\ - 2 - 2 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.5

Subtrahiere $3$ von $- 3$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 2 \\ - 6 & - 12 - 12 & 10 + 10 & 6 + 6 \\ 0 + 0 & - 2 - 2 & 2 + 2 & 1 + 1 \\ - 2 - 2 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.6

Subtrahiere $12$ von $- 12$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 2 \\ - 6 & - 24 & 10 + 10 & 6 + 6 \\ 0 + 0 & - 2 - 2 & 2 + 2 & 1 + 1 \\ - 2 - 2 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.7

Addiere $10$ und $10$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 2 \\ - 6 & - 24 & 20 & 6 + 6 \\ 0 + 0 & - 2 - 2 & 2 + 2 & 1 + 1 \\ - 2 - 2 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.8

Addiere $6$ und $6$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 2 \\ - 6 & - 24 & 20 & 12 \\ 0 + 0 & - 2 - 2 & 2 + 2 & 1 + 1 \\ - 2 - 2 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.9

Addiere $0$ und $0$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 2 \\ - 6 & - 24 & 20 & 12 \\ 0 & - 2 - 2 & 2 + 2 & 1 + 1 \\ - 2 - 2 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.10

Subtrahiere $2$ von $- 2$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 2 \\ - 6 & - 24 & 20 & 12 \\ 0 & - 4 & 2 + 2 & 1 + 1 \\ - 2 - 2 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.11

Addiere $2$ und $2$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 2 \\ - 6 & - 24 & 20 & 12 \\ 0 & - 4 & 4 & 1 + 1 \\ - 2 - 2 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.12

Addiere $1$ und $1$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 2 \\ - 6 & - 24 & 20 & 12 \\ 0 & - 4 & 4 & 2 \\ - 2 - 2 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.13

Subtrahiere $2$ von $- 2$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 2 \\ - 6 & - 24 & 20 & 12 \\ 0 & - 4 & 4 & 2 \\ - 4 & - 6 - 6 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.14

Subtrahiere $6$ von $- 6$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 2 \\ - 6 & - 24 & 20 & 12 \\ 0 & - 4 & 4 & 2 \\ - 4 & - 12 & 5 + 5 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.15

Addiere $5$ und $5$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 2 \\ - 6 & - 24 & 20 & 12 \\ 0 & - 4 & 4 & 2 \\ - 4 & - 12 & 10 & 3 + 3 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 5.16

Addiere $3$ und $3$ .

$[\begin{array}{c} 2 & 6 & - 4 & - 2 \\ - 6 & - 24 & 20 & 12 \\ 0 & - 4 & 4 & 2 \\ - 4 & - 12 & 10 & 6 \end{array}] + [\begin{array}{c} 0 & 1 & 0 & 2 \\ 1 & - 1 & - 2 & 2 \\ 0 & 1 & 3 & - 3 \\ - 2 & 2 & 3 & - 2 \end{array}]$

Schritt 6

Addiere die entsprechenden Elemente.

$[\begin{array}{c} 2 + 0 & 6 + 1 & - 4 + 0 & - 2 + 2 \\ - 6 + 1 & - 24 - 1 & 20 - 2 & 12 + 2 \\ 0 + 0 & - 4 + 1 & 4 + 3 & 2 - 3 \\ - 4 - 2 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7

Simplify each element.

Tippen, um mehr Schritte zu sehen ...

Schritt 7.1

Addiere $2$ und $0$ .

$[\begin{array}{c} 2 & 6 + 1 & - 4 + 0 & - 2 + 2 \\ - 6 + 1 & - 24 - 1 & 20 - 2 & 12 + 2 \\ 0 + 0 & - 4 + 1 & 4 + 3 & 2 - 3 \\ - 4 - 2 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.2

Addiere $6$ und $1$ .

$[\begin{array}{c} 2 & 7 & - 4 + 0 & - 2 + 2 \\ - 6 + 1 & - 24 - 1 & 20 - 2 & 12 + 2 \\ 0 + 0 & - 4 + 1 & 4 + 3 & 2 - 3 \\ - 4 - 2 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.3

Addiere $- 4$ und $0$ .

$[\begin{array}{c} 2 & 7 & - 4 & - 2 + 2 \\ - 6 + 1 & - 24 - 1 & 20 - 2 & 12 + 2 \\ 0 + 0 & - 4 + 1 & 4 + 3 & 2 - 3 \\ - 4 - 2 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.4

Addiere $- 2$ und $2$ .

$[\begin{array}{c} 2 & 7 & - 4 & 0 \\ - 6 + 1 & - 24 - 1 & 20 - 2 & 12 + 2 \\ 0 + 0 & - 4 + 1 & 4 + 3 & 2 - 3 \\ - 4 - 2 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.5

Addiere $- 6$ und $1$ .

$[\begin{array}{c} 2 & 7 & - 4 & 0 \\ - 5 & - 24 - 1 & 20 - 2 & 12 + 2 \\ 0 + 0 & - 4 + 1 & 4 + 3 & 2 - 3 \\ - 4 - 2 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.6

Subtrahiere $1$ von $- 24$ .

$[\begin{array}{c} 2 & 7 & - 4 & 0 \\ - 5 & - 25 & 20 - 2 & 12 + 2 \\ 0 + 0 & - 4 + 1 & 4 + 3 & 2 - 3 \\ - 4 - 2 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.7

Subtrahiere $2$ von $20$ .

$[\begin{array}{c} 2 & 7 & - 4 & 0 \\ - 5 & - 25 & 18 & 12 + 2 \\ 0 + 0 & - 4 + 1 & 4 + 3 & 2 - 3 \\ - 4 - 2 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.8

Addiere $12$ und $2$ .

$[\begin{array}{c} 2 & 7 & - 4 & 0 \\ - 5 & - 25 & 18 & 14 \\ 0 + 0 & - 4 + 1 & 4 + 3 & 2 - 3 \\ - 4 - 2 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.9

Addiere $0$ und $0$ .

$[\begin{array}{c} 2 & 7 & - 4 & 0 \\ - 5 & - 25 & 18 & 14 \\ 0 & - 4 + 1 & 4 + 3 & 2 - 3 \\ - 4 - 2 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.10

Addiere $- 4$ und $1$ .

$[\begin{array}{c} 2 & 7 & - 4 & 0 \\ - 5 & - 25 & 18 & 14 \\ 0 & - 3 & 4 + 3 & 2 - 3 \\ - 4 - 2 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.11

Addiere $4$ und $3$ .

$[\begin{array}{c} 2 & 7 & - 4 & 0 \\ - 5 & - 25 & 18 & 14 \\ 0 & - 3 & 7 & 2 - 3 \\ - 4 - 2 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.12

Subtrahiere $3$ von $2$ .

$[\begin{array}{c} 2 & 7 & - 4 & 0 \\ - 5 & - 25 & 18 & 14 \\ 0 & - 3 & 7 & - 1 \\ - 4 - 2 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.13

Subtrahiere $2$ von $- 4$ .

$[\begin{array}{c} 2 & 7 & - 4 & 0 \\ - 5 & - 25 & 18 & 14 \\ 0 & - 3 & 7 & - 1 \\ - 6 & - 12 + 2 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.14

Addiere $- 12$ und $2$ .

$[\begin{array}{c} 2 & 7 & - 4 & 0 \\ - 5 & - 25 & 18 & 14 \\ 0 & - 3 & 7 & - 1 \\ - 6 & - 10 & 10 + 3 & 6 - 2 \end{array}]$

Schritt 7.15

Addiere $10$ und $3$ .

$[\begin{array}{c} 2 & 7 & - 4 & 0 \\ - 5 & - 25 & 18 & 14 \\ 0 & - 3 & 7 & - 1 \\ - 6 & - 10 & 13 & 6 - 2 \end{array}]$

Schritt 7.16

Subtrahiere $2$ von $6$ .

$[\begin{array}{c} 2 & 7 & - 4 & 0 \\ - 5 & - 25 & 18 & 14 \\ 0 & - 3 & 7 & - 1 \\ - 6 & - 10 & 13 & 4 \end{array}]$