Lineare Algebra Beispiele

$[\begin{array}{c} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}] - [\begin{array}{c} - 1 & 2 & 0 & 1 \\ 1 & 2 & 1 & 1 \\ 0 & 1 & 1 & - 1 \\ 0 & 0 & 1 & 2 \end{array}]$

Schritt 1

Subtrahiere die entsprechenden Elemente.

$[\begin{array}{c} 1 + 1 & 0 - 2 & 0 - 0 & 0 - 1 \\ 0 - 1 & 1 - 2 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2

Simplify each element.

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Schritt 2.1

Addiere $1$ und $1$ .

$[\begin{array}{c} 2 & 0 - 2 & 0 - 0 & 0 - 1 \\ 0 - 1 & 1 - 2 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.2

Subtrahiere $2$ von $0$ .

$[\begin{array}{c} 2 & - 2 & 0 - 0 & 0 - 1 \\ 0 - 1 & 1 - 2 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.3

Subtrahiere $0$ von $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & 0 - 1 \\ 0 - 1 & 1 - 2 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.4

Subtrahiere $1$ von $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ 0 - 1 & 1 - 2 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.5

Subtrahiere $1$ von $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & 1 - 2 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.6

Subtrahiere $2$ von $1$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & 0 - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.7

Subtrahiere $1$ von $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & 0 - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.8

Subtrahiere $1$ von $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 - 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.9

Subtrahiere $0$ von $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & 0 - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.10

Subtrahiere $1$ von $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 1 - 1 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.11

Subtrahiere $1$ von $1$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 0 & 0 + 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.12

Addiere $0$ und $1$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 0 & 1 \\ 0 - 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.13

Subtrahiere $0$ von $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 0 & 1 \\ 0 & 0 - 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.14

Subtrahiere $0$ von $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 0 & 1 \\ 0 & 0 & 0 - 1 & 1 - 2 \end{array}]$

Schritt 2.15

Subtrahiere $1$ von $0$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 0 & 1 \\ 0 & 0 & - 1 & 1 - 2 \end{array}]$

Schritt 2.16

Subtrahiere $2$ von $1$ .

$[\begin{array}{c} 2 & - 2 & 0 & - 1 \\ - 1 & - 1 & - 1 & - 1 \\ 0 & - 1 & 0 & 1 \\ 0 & 0 & - 1 & - 1 \end{array}]$