Ensembles finis Exemples

$[\begin{array}{c} 0 & 0 & 0.36 & 920 \\ 0.17 & 0 & 0 & 280 \\ 0 & 0.7 & 0.93 & 2800 \end{array}]$

Étape 1

Swap $R_{2}$ with $R_{1}$ to put a nonzero entry at $1, 1$ .

$[\begin{array}{c} 0.17 & 0 & 0 & 280 \\ 0 & 0 & 0.36 & 920 \\ 0 & 0.7 & 0.93 & 2800 \end{array}]$

Étape 2

Multiply each element of $R_{1}$ by $\frac{1}{0.17}$ to make the entry at $1, 1$ a $1$ .

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Étape 2.1

Multiply each element of $R_{1}$ by $\frac{1}{0.17}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{0.17}{0.17} & \frac{0}{0.17} & \frac{0}{0.17} & \frac{280}{0.17} \\ 0 & 0 & 0.36 & 920 \\ 0 & 0.7 & 0.93 & 2800 \end{array}]$

Étape 2.2

Simplifiez $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & 1647.05882352 \\ 0 & 0 & 0.36 & 920 \\ 0 & 0.7 & 0.93 & 2800 \end{array}]$

Étape 3

Swap $R_{3}$ with $R_{2}$ to put a nonzero entry at $2, 2$ .

$[\begin{array}{c} 1 & 0 & 0 & 1647.05882352 \\ 0 & 0.7 & 0.93 & 2800 \\ 0 & 0 & 0.36 & 920 \end{array}]$

Étape 4

Multiply each element of $R_{2}$ by $\frac{1}{0.7}$ to make the entry at $2, 2$ a $1$ .

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Étape 4.1

Multiply each element of $R_{2}$ by $\frac{1}{0.7}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 0 & 0 & 1647.05882352 \\ \frac{0}{0.7} & \frac{0.7}{0.7} & \frac{0.93}{0.7} & \frac{2800}{0.7} \\ 0 & 0 & 0.36 & 920 \end{array}]$

Étape 4.2

Simplifiez $R_{2}$ .

$[\begin{array}{c} 1 & 0 & 0 & 1647.05882352 \\ 0 & 1 & 1.3\overline{285714} & 4000 \\ 0 & 0 & 0.36 & 920 \end{array}]$

Étape 5

Multiply each element of $R_{3}$ by $\frac{1}{0.36}$ to make the entry at $3, 3$ a $1$ .

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Étape 5.1

Multiply each element of $R_{3}$ by $\frac{1}{0.36}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 0 & 0 & 1647.05882352 \\ 0 & 1 & 1.3\overline{285714} & 4000 \\ \frac{0}{0.36} & \frac{0}{0.36} & \frac{0.36}{0.36} & \frac{920}{0.36} \end{array}]$

Étape 5.2

Simplifiez $R_{3}$ .

$[\begin{array}{c} 1 & 0 & 0 & 1647.05882352 \\ 0 & 1 & 1.3\overline{285714} & 4000 \\ 0 & 0 & 1 & 2555.\overline{5} \end{array}]$

Étape 6

Perform the row operation $R_{2} = R_{2} - 1.3\overline{285714} R_{3}$ to make the entry at $2, 3$ a $0$ .

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Étape 6.1

Perform the row operation $R_{2} = R_{2} - 1.3\overline{285714} R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 0 & 0 & 1647.05882352 \\ 0 - 1.3\overline{285714} \cdot 0 & 1 - 1.3\overline{285714} \cdot 0 & 1.3\overline{285714} - 1.3\overline{285714} \cdot 1 & 4000 - 1.3\overline{285714} \cdot 2555.\overline{5} \\ 0 & 0 & 1 & 2555.\overline{5} \end{array}]$

Étape 6.2

Simplifiez $R_{2}$ .

$[\begin{array}{c} 1 & 0 & 0 & 1647.05882352 \\ 0 & 1 & 0 & 604.\overline{761904} \\ 0 & 0 & 1 & 2555.\overline{5} \end{array}]$