有限数学示例

$[\begin{array}{c} 1 & 1 & 27000 \\ 30 & 90 & 49500 \\ 0.5 & 2 & 0 \end{array}]$

解题步骤 1

Perform the row operation $R_{2} = R_{2} - 30 R_{1}$ to make the entry at $2, 1$ a $0$ .

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解题步骤 1.1

Perform the row operation $R_{2} = R_{2} - 30 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 1 & 27000 \\ 30 - 30 \cdot 1 & 90 - 30 \cdot 1 & 49500 - 30 \cdot 27000 \\ 0.5 & 2 & 0 \end{array}]$

解题步骤 1.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 1 & 27000 \\ 0 & 60 & - 760500 \\ 0.5 & 2 & 0 \end{array}]$

解题步骤 2

Perform the row operation $R_{3} = R_{3} - 0.5 R_{1}$ to make the entry at $3, 1$ a $0$ .

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解题步骤 2.1

Perform the row operation $R_{3} = R_{3} - 0.5 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 1 & 27000 \\ 0 & 60 & - 760500 \\ 0.5 - 0.5 \cdot 1 & 2 - 0.5 \cdot 1 & 0 - 0.5 \cdot 27000 \end{array}]$

解题步骤 2.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 1 & 27000 \\ 0 & 60 & - 760500 \\ 0 & 1.5 & - 13500 \end{array}]$

解题步骤 3

Multiply each element of $R_{2}$ by $\frac{1}{60}$ to make the entry at $2, 2$ a $1$ .

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解题步骤 3.1

Multiply each element of $R_{2}$ by $\frac{1}{60}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 1 & 27000 \\ \frac{0}{60} & \frac{60}{60} & \frac{- 760500}{60} \\ 0 & 1.5 & - 13500 \end{array}]$

解题步骤 3.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 1 & 27000 \\ 0 & 1 & - 12675 \\ 0 & 1.5 & - 13500 \end{array}]$

解题步骤 4

Perform the row operation $R_{3} = R_{3} - 1.5 R_{2}$ to make the entry at $3, 2$ a $0$ .

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解题步骤 4.1

Perform the row operation $R_{3} = R_{3} - 1.5 R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & 1 & 27000 \\ 0 & 1 & - 12675 \\ 0 - 1.5 \cdot 0 & 1.5 - 1.5 \cdot 1 & - 13500 - 1.5 \cdot - 12675 \end{array}]$

解题步骤 4.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 1 & 27000 \\ 0 & 1 & - 12675 \\ 0 & 0 & 5512.5 \end{array}]$

解题步骤 5

Multiply each element of $R_{3}$ by $\frac{1}{5512.5}$ to make the entry at $3, 3$ a $1$ .

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解题步骤 5.1

Multiply each element of $R_{3}$ by $\frac{1}{5512.5}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 1 & 27000 \\ 0 & 1 & - 12675 \\ \frac{0}{5512.5} & \frac{0}{5512.5} & \frac{5512.5}{5512.5} \end{array}]$

解题步骤 5.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 1 & 27000 \\ 0 & 1 & - 12675 \\ 0 & 0 & 1 \end{array}]$

解题步骤 6

Perform the row operation $R_{2} = R_{2} + 12675 R_{3}$ to make the entry at $2, 3$ a $0$ .

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解题步骤 6.1

Perform the row operation $R_{2} = R_{2} + 12675 R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 1 & 27000 \\ 0 + 12675 \cdot 0 & 1 + 12675 \cdot 0 & - 12675 + 12675 \cdot 1 \\ 0 & 0 & 1 \end{array}]$

解题步骤 6.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 1 & 27000 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

解题步骤 7

Perform the row operation $R_{1} = R_{1} - 27000 R_{3}$ to make the entry at $1, 3$ a $0$ .

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解题步骤 7.1

Perform the row operation $R_{1} = R_{1} - 27000 R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 - 27000 \cdot 0 & 1 - 27000 \cdot 0 & 27000 - 27000 \cdot 1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

解题步骤 7.2

化简 $R_{1}$ 。

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

解题步骤 8

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

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解题步骤 8.1

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

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

解题步骤 8.2

化简 $R_{1}$ 。

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

有限数学 示例

有限数学示例