الرياضيات المتناهية الأمثلة

$[\begin{array}{c} 2 & 0 & - 2 & 0 \\ 1 & 1 & 1 & 18500 \\ 0.11 & 0.07 & 0.05 & 1565 \end{array}]$

خطوة 1

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

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خطوة 1.1

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

$[\begin{array}{c} \frac{2}{2} & \frac{0}{2} & \frac{- 2}{2} & \frac{0}{2} \\ 1 & 1 & 1 & 18500 \\ 0.11 & 0.07 & 0.05 & 1565 \end{array}]$

خطوة 1.2

بسّط $R_{1}$ .

$[\begin{array}{c} 1 & 0 & - 1 & 0 \\ 1 & 1 & 1 & 18500 \\ 0.11 & 0.07 & 0.05 & 1565 \end{array}]$

خطوة 2

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

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خطوة 2.1

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

$[\begin{array}{c} 1 & 0 & - 1 & 0 \\ 1 - 1 & 1 - 0 & 1 + 1 & 18500 - 0 \\ 0.11 & 0.07 & 0.05 & 1565 \end{array}]$

خطوة 2.2

بسّط $R_{2}$ .

$[\begin{array}{c} 1 & 0 & - 1 & 0 \\ 0 & 1 & 2 & 18500 \\ 0.11 & 0.07 & 0.05 & 1565 \end{array}]$

خطوة 3

Perform the row operation $R_{3} = R_{3} - 0.11 R_{1}$ to make the entry at $3, 1$ a $0$ .

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خطوة 3.1

Perform the row operation $R_{3} = R_{3} - 0.11 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 0 & - 1 & 0 \\ 0 & 1 & 2 & 18500 \\ 0.11 - 0.11 \cdot 1 & 0.07 - 0.11 \cdot 0 & 0.05 - 0.11 \cdot - 1 & 1565 - 0.11 \cdot 0 \end{array}]$

خطوة 3.2

بسّط $R_{3}$ .

$[\begin{array}{c} 1 & 0 & - 1 & 0 \\ 0 & 1 & 2 & 18500 \\ 0 & 0.07 & 0.16 & 1565 \end{array}]$

خطوة 4

Perform the row operation $R_{3} = R_{3} - 0.07 R_{2}$ to make the entry at $3, 2$ a $0$ .

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خطوة 4.1

Perform the row operation $R_{3} = R_{3} - 0.07 R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & 0 & - 1 & 0 \\ 0 & 1 & 2 & 18500 \\ 0 - 0.07 \cdot 0 & 0.07 - 0.07 \cdot 1 & 0.16 - 0.07 \cdot 2 & 1565 - 0.07 \cdot 18500 \end{array}]$

خطوة 4.2

بسّط $R_{3}$ .

$[\begin{array}{c} 1 & 0 & - 1 & 0 \\ 0 & 1 & 2 & 18500 \\ 0 & 0 & 0.02 & 270 \end{array}]$

خطوة 5

Multiply each element of $R_{3}$ by $\frac{1}{0.02}$ to make the entry at $3, 3$ a $1$ .

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خطوة 5.1

Multiply each element of $R_{3}$ by $\frac{1}{0.02}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 0 & - 1 & 0 \\ 0 & 1 & 2 & 18500 \\ \frac{0}{0.02} & \frac{0}{0.02} & \frac{0.02}{0.02} & \frac{270}{0.02} \end{array}]$

خطوة 5.2

بسّط $R_{3}$ .

$[\begin{array}{c} 1 & 0 & - 1 & 0 \\ 0 & 1 & 2 & 18500 \\ 0 & 0 & 1 & 13500 \end{array}]$

خطوة 6

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

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خطوة 6.1

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

$[\begin{array}{c} 1 & 0 & - 1 & 0 \\ 0 - 2 \cdot 0 & 1 - 2 \cdot 0 & 2 - 2 \cdot 1 & 18500 - 2 \cdot 13500 \\ 0 & 0 & 1 & 13500 \end{array}]$

خطوة 6.2

بسّط $R_{2}$ .

$[\begin{array}{c} 1 & 0 & - 1 & 0 \\ 0 & 1 & 0 & - 8500 \\ 0 & 0 & 1 & 13500 \end{array}]$

خطوة 7

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

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خطوة 7.1

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

$[\begin{array}{c} 1 + 0 & 0 + 0 & - 1 + 1 \cdot 1 & 0 + 1 \cdot 13500 \\ 0 & 1 & 0 & - 8500 \\ 0 & 0 & 1 & 13500 \end{array}]$

خطوة 7.2

بسّط $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & 13500 \\ 0 & 1 & 0 & - 8500 \\ 0 & 0 & 1 & 13500 \end{array}]$