Lineare Algebra Beispiele

$[\begin{array}{c} 1 & - 3 & 5 & - 2 \\ 2 & - 1 & 5 & 6 \end{array}]$

Schritt 1

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

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Schritt 1.1

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

$[\begin{array}{c} 1 & - 3 & 5 & - 2 \\ 2 - 2 \cdot 1 & - 1 - 2 \cdot - 3 & 5 - 2 \cdot 5 & 6 - 2 \cdot - 2 \end{array}]$

Schritt 1.2

Vereinfache $R_{2}$ .

$[\begin{array}{c} 1 & - 3 & 5 & - 2 \\ 0 & 5 & - 5 & 10 \end{array}]$

Schritt 2

Multiply each element of $R_{2}$ by $\frac{1}{5}$ to make the entry at $2, 2$ a $1$ .

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Schritt 2.1

Multiply each element of $R_{2}$ by $\frac{1}{5}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - 3 & 5 & - 2 \\ \frac{0}{5} & \frac{5}{5} & \frac{- 5}{5} & \frac{10}{5} \end{array}]$

Schritt 2.2

Vereinfache $R_{2}$ .

$[\begin{array}{c} 1 & - 3 & 5 & - 2 \\ 0 & 1 & - 1 & 2 \end{array}]$

Schritt 3

Perform the row operation $R_{1} = R_{1} + 3 R_{2}$ to make the entry at $1, 2$ a $0$ .

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Schritt 3.1

Perform the row operation $R_{1} = R_{1} + 3 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 + 3 \cdot 0 & - 3 + 3 \cdot 1 & 5 + 3 \cdot - 1 & - 2 + 3 \cdot 2 \\ 0 & 1 & - 1 & 2 \end{array}]$

Schritt 3.2

Vereinfache $R_{1}$ .

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