Elementarmathematik Beispiele

$[\begin{array}{c} 1 & 1 & 11000 \\ 0.7 & 0.8 & 865 \end{array}]$

Schritt 1

Perform the row operation $R_{2} = R_{2} - 0.7 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Schritt 1.1

Perform the row operation $R_{2} = R_{2} - 0.7 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 1 & 11000 \\ 0.7 - 0.7 \cdot 1 & 0.8 - 0.7 \cdot 1 & 865 - 0.7 \cdot 11000 \end{array}]$

Schritt 1.2

Vereinfache $R_{2}$ .

$[\begin{array}{c} 1 & 1 & 11000 \\ 0 & 0.1 & - 6835 \end{array}]$

Schritt 2

Multiply each element of $R_{2}$ by $\frac{1}{0.1}$ to make the entry at $2, 2$ a $1$ .

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Schritt 2.1

Multiply each element of $R_{2}$ by $\frac{1}{0.1}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 1 & 11000 \\ \frac{0}{0.1} & \frac{0.1}{0.1} & \frac{- 6835}{0.1} \end{array}]$

Schritt 2.2

Vereinfache $R_{2}$ .

$[\begin{array}{c} 1 & 1 & 11000 \\ 0 & 1 & - 68350 \end{array}]$

Schritt 3

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

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Schritt 3.1

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

$[\begin{array}{c} 1 - 0 & 1 - 1 & 11000 + 68350 \\ 0 & 1 & - 68350 \end{array}]$

Schritt 3.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 79350 \\ 0 & 1 & - 68350 \end{array}]$