Finite Mathematik Beispiele

$[\begin{array}{c} 7 & 0 & 0 & 14 \\ 0 & 8 & 0 & 3 \\ 0 & 0 & 6 & 5 \end{array}]$

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 $1$ .

$[\begin{array}{c} \frac{7}{7} & \frac{0}{7} & \frac{0}{7} & \frac{14}{7} \\ 0 & 8 & 0 & 3 \\ 0 & 0 & 6 & 5 \end{array}]$

Schritt 1.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & 2 \\ 0 & 8 & 0 & 3 \\ 0 & 0 & 6 & 5 \end{array}]$

Schritt 2

Multiply each element of $R_{2}$ by $\frac{1}{8}$ to make the entry at $2, 2$ a $1$ .

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Schritt 2.1

Multiply each element of $R_{2}$ by $\frac{1}{8}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 0 & 0 & 2 \\ \frac{0}{8} & \frac{8}{8} & \frac{0}{8} & \frac{3}{8} \\ 0 & 0 & 6 & 5 \end{array}]$

Schritt 2.2

Vereinfache $R_{2}$ .

$[\begin{array}{c} 1 & 0 & 0 & 2 \\ 0 & 1 & 0 & \frac{3}{8} \\ 0 & 0 & 6 & 5 \end{array}]$

Schritt 3

Multiply each element of $R_{3}$ by $\frac{1}{6}$ to make the entry at $3, 3$ a $1$ .

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Schritt 3.1

Multiply each element of $R_{3}$ by $\frac{1}{6}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 0 & 0 & 2 \\ 0 & 1 & 0 & \frac{3}{8} \\ \frac{0}{6} & \frac{0}{6} & \frac{6}{6} & \frac{5}{6} \end{array}]$

Schritt 3.2

Vereinfache $R_{3}$ .

$[\begin{array}{c} 1 & 0 & 0 & 2 \\ 0 & 1 & 0 & \frac{3}{8} \\ 0 & 0 & 1 & \frac{5}{6} \end{array}]$