Lineare Algebra Beispiele

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

Schritt 1

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

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Schritt 1.1

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

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

Schritt 1.2

Vereinfache $R_{2}$ .

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

Schritt 2

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

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Schritt 2.1

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

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

Schritt 2.2

Vereinfache $R_{2}$ .

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

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 $0$ .

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

Schritt 3.2

Vereinfache $R_{1}$ .

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