Beispiele

x - [\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}] = [\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}]

$x - [\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}] = [\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}]$

Schritt 1

Move all terms not containing a variable to the right side.

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Schritt 1.1

Addiere

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

$[\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]$ zu beiden Seiten der Gleichung.

x = [\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}] + [\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]

$x = [\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}] + [\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]$

x = [\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}] + [\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]

$x = [\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}] + [\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]$

Schritt 2

Vereinfache die rechte Seite.

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Schritt 2.1

Addiere die entsprechenden Elemente.

x = [\begin{array}{c} 2 + 1 & 2 - 1 & 2 + 0 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]

$x = [\begin{array}{c} 2 + 1 & 2 - 1 & 2 + 0 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]$

Schritt 2.2

Simplify each element.

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Schritt 2.2.1

Addiere

2

$2$ und

1

$1$ .

x = [\begin{array}{c} 3 & 2 - 1 & 2 + 0 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]

$x = [\begin{array}{c} 3 & 2 - 1 & 2 + 0 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]$

Schritt 2.2.2

Subtrahiere

1

$1$ von

2

$2$ .

x = [\begin{array}{c} 3 & 1 & 2 + 0 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 + 0 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]$

Schritt 2.2.3

Addiere

2

$2$ und

0

$0$ .

x = [\begin{array}{c} 3 & 1 & 2 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]$

Schritt 2.2.4

Addiere

8

$8$ und

0

$0$ .

x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 3 + 1 & 4 + 1 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 3 + 1 & 4 + 1 \end{array}]$

Schritt 2.2.5

Addiere

3

$3$ und

1

$1$ .

x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 4 + 1 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 4 + 1 \end{array}]$

Schritt 2.2.6

Addiere

4

$4$ und

1

$1$ .

x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]$

x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]$

x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]$

Gib DEINE Aufgabe ein