Finite Mathematik Beispiele

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 8 & 9 & 10 & 227000 \\ 0 & 0 & 1 & 5000 \end{array}]$

Schritt 1

Perform the row operation $R_{2} = R_{2} - 8 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Schritt 1.1

Perform the row operation $R_{2} = R_{2} - 8 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 8 - 8 \cdot 1 & 9 - 8 \cdot 1 & 10 - 8 \cdot 1 & 227000 - 8 \cdot 26000 \\ 0 & 0 & 1 & 5000 \end{array}]$

Schritt 1.2

Vereinfache $R_{2}$ .

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 0 & 1 & 2 & 19000 \\ 0 & 0 & 1 & 5000 \end{array}]$

Schritt 2

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

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Schritt 2.1

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

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 0 - 2 \cdot 0 & 1 - 2 \cdot 0 & 2 - 2 \cdot 1 & 19000 - 2 \cdot 5000 \\ 0 & 0 & 1 & 5000 \end{array}]$

Schritt 2.2

Vereinfache $R_{2}$ .

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 0 & 1 & 0 & 9000 \\ 0 & 0 & 1 & 5000 \end{array}]$

Schritt 3

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

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Schritt 3.1

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

$[\begin{array}{c} 1 - 0 & 1 - 0 & 1 - 1 & 26000 - 5000 \\ 0 & 1 & 0 & 9000 \\ 0 & 0 & 1 & 5000 \end{array}]$

Schritt 3.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & 1 & 0 & 21000 \\ 0 & 1 & 0 & 9000 \\ 0 & 0 & 1 & 5000 \end{array}]$

Schritt 4

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

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Schritt 4.1

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

$[\begin{array}{c} 1 - 0 & 1 - 1 & 0 - 0 & 21000 - 9000 \\ 0 & 1 & 0 & 9000 \\ 0 & 0 & 1 & 5000 \end{array}]$

Schritt 4.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & 12000 \\ 0 & 1 & 0 & 9000 \\ 0 & 0 & 1 & 5000 \end{array}]$