Lineare Algebra Beispiele

$[\begin{array}{c} 1 & 2 & - 9 & - 8 \\ 0 & 1 & 7 & - 3 \\ 0 & 0 & 1 & 7 \end{array}]$

Schritt 1

Perform the row operation $R_{2} = R_{2} - 7 R_{3}$ to make the entry at $2, 3$ a $0$ .

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Schritt 1.1

Perform the row operation $R_{2} = R_{2} - 7 R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 2 & - 9 & - 8 \\ 0 - 7 \cdot 0 & 1 - 7 \cdot 0 & 7 - 7 \cdot 1 & - 3 - 7 \cdot 7 \\ 0 & 0 & 1 & 7 \end{array}]$

Schritt 1.2

Vereinfache $R_{2}$ .

$[\begin{array}{c} 1 & 2 & - 9 & - 8 \\ 0 & 1 & 0 & - 52 \\ 0 & 0 & 1 & 7 \end{array}]$

Schritt 2

Perform the row operation $R_{1} = R_{1} + 9 R_{3}$ to make the entry at $1, 3$ a $0$ .

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Schritt 2.1

Perform the row operation $R_{1} = R_{1} + 9 R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 + 9 \cdot 0 & 2 + 9 \cdot 0 & - 9 + 9 \cdot 1 & - 8 + 9 \cdot 7 \\ 0 & 1 & 0 & - 52 \\ 0 & 0 & 1 & 7 \end{array}]$

Schritt 2.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & 2 & 0 & 55 \\ 0 & 1 & 0 & - 52 \\ 0 & 0 & 1 & 7 \end{array}]$

Schritt 3

Perform the row operation $R_{1} = R_{1} - 2 R_{2}$ to make the entry at $1, 2$ a $0$ .

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Schritt 3.1

Perform the row operation $R_{1} = R_{1} - 2 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - 2 \cdot 0 & 2 - 2 \cdot 1 & 0 - 2 \cdot 0 & 55 - 2 \cdot - 52 \\ 0 & 1 & 0 & - 52 \\ 0 & 0 & 1 & 7 \end{array}]$

Schritt 3.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & 159 \\ 0 & 1 & 0 & - 52 \\ 0 & 0 & 1 & 7 \end{array}]$