Lineare Algebra Beispiele

$[\begin{array}{c} 7 & 4 & 1 \\ 0 & 1 & 2 \end{array}]$

Schritt 1

Multiply each element of $R_{1}$ by $\frac{1}{7}$ to make the entry at $1, 1$ a $1$ .

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Schritt 1.1

Multiply each element of $R_{1}$ by $\frac{1}{7}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{7}{7} & \frac{4}{7} & \frac{1}{7} \\ 0 & 1 & 2 \end{array}]$

Schritt 1.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & \frac{4}{7} & \frac{1}{7} \\ 0 & 1 & 2 \end{array}]$

Schritt 2

Perform the row operation $R_{1} = R_{1} - \frac{4}{7} R_{2}$ to make the entry at $1, 2$ a $0$ .

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Schritt 2.1

Perform the row operation $R_{1} = R_{1} - \frac{4}{7} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{4}{7} \cdot 0 & \frac{4}{7} - \frac{4}{7} \cdot 1 & \frac{1}{7} - \frac{4}{7} \cdot 2 \\ 0 & 1 & 2 \end{array}]$

Schritt 2.2

Vereinfache $R_{1}$ .

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