Finite Mathematik Beispiele

$[\begin{array}{c} 3 & - 2 & 1 & 16 \\ 0 & 1 & 1 & 7 \end{array}]$

Schritt 1

Multiply each element of $R_{1}$ by $\frac{1}{3}$ to make the entry at $1, 1$ a $1$ .

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Schritt 1.1

Multiply each element of $R_{1}$ by $\frac{1}{3}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{3}{3} & \frac{- 2}{3} & \frac{1}{3} & \frac{16}{3} \\ 0 & 1 & 1 & 7 \end{array}]$

Schritt 1.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & - \frac{2}{3} & \frac{1}{3} & \frac{16}{3} \\ 0 & 1 & 1 & 7 \end{array}]$

Schritt 2

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

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Schritt 2.1

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

$[\begin{array}{c} 1 + \frac{2}{3} \cdot 0 & - \frac{2}{3} + \frac{2}{3} \cdot 1 & \frac{1}{3} + \frac{2}{3} \cdot 1 & \frac{16}{3} + \frac{2}{3} \cdot 7 \\ 0 & 1 & 1 & 7 \end{array}]$

Schritt 2.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 1 & 10 \\ 0 & 1 & 1 & 7 \end{array}]$