الرياضيات المتناهية الأمثلة

$[\begin{array}{c} 1 & 1 & 1 & 19 \\ 4 & 5 & 8 & 27 \end{array}]$

خطوة 1

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

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خطوة 1.1

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 1 & 1 & 19 \\ 4 - 4 \cdot 1 & 5 - 4 \cdot 1 & 8 - 4 \cdot 1 & 27 - 4 \cdot 19 \end{array}]$

خطوة 1.2

بسّط $R_{2}$ .

$[\begin{array}{c} 1 & 1 & 1 & 19 \\ 0 & 1 & 4 & - 49 \end{array}]$

خطوة 2

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

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خطوة 2.1

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

$[\begin{array}{c} 1 - 0 & 1 - 1 & 1 - 4 & 19 + 49 \\ 0 & 1 & 4 & - 49 \end{array}]$

خطوة 2.2

بسّط $R_{1}$ .

$[\begin{array}{c} 1 & 0 & - 3 & 68 \\ 0 & 1 & 4 & - 49 \end{array}]$