有限数学示例

$[\begin{array}{c} 0.2 & 0.03 & 0.07 & 0.3 \\ 0.28 & 0.05 & 0.07 & 0.4 \\ 0.22 & 0.01 & 0.07 & 1 \end{array}]$

解题步骤 1

Multiply each element of $R_{1}$ by $\frac{1}{0.2}$ to make the entry at $1, 1$ a $1$ .

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解题步骤 1.1

Multiply each element of $R_{1}$ by $\frac{1}{0.2}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{0.2}{0.2} & \frac{0.03}{0.2} & \frac{0.07}{0.2} & \frac{0.3}{0.2} \\ 0.28 & 0.05 & 0.07 & 0.4 \\ 0.22 & 0.01 & 0.07 & 1 \end{array}]$

解题步骤 1.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & 0.15 & 0.35 & 1.5 \\ 0.28 & 0.05 & 0.07 & 0.4 \\ 0.22 & 0.01 & 0.07 & 1 \end{array}]$

解题步骤 2

Perform the row operation $R_{2} = R_{2} - 0.28 R_{1}$ to make the entry at $2, 1$ a $0$ .

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解题步骤 2.1

Perform the row operation $R_{2} = R_{2} - 0.28 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 0.15 & 0.35 & 1.5 \\ 0.28 - 0.28 \cdot 1 & 0.05 - 0.28 \cdot 0.15 & 0.07 - 0.28 \cdot 0.35 & 0.4 - 0.28 \cdot 1.5 \\ 0.22 & 0.01 & 0.07 & 1 \end{array}]$

解题步骤 2.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 0.15 & 0.35 & 1.5 \\ 0 & 0.008 & - 0.028 & - 0.02 \\ 0.22 & 0.01 & 0.07 & 1 \end{array}]$

解题步骤 3

Perform the row operation $R_{3} = R_{3} - 0.22 R_{1}$ to make the entry at $3, 1$ a $0$ .

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解题步骤 3.1

Perform the row operation $R_{3} = R_{3} - 0.22 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 0.15 & 0.35 & 1.5 \\ 0 & 0.008 & - 0.028 & - 0.02 \\ 0.22 - 0.22 \cdot 1 & 0.01 - 0.22 \cdot 0.15 & 0.07 - 0.22 \cdot 0.35 & 1 - 0.22 \cdot 1.5 \end{array}]$

解题步骤 3.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 0.15 & 0.35 & 1.5 \\ 0 & 0.008 & - 0.028 & - 0.02 \\ 0 & - 0.023 & - 0.007 & 0.67 \end{array}]$

解题步骤 4

Multiply each element of $R_{2}$ by $\frac{1}{0.008}$ to make the entry at $2, 2$ a $1$ .

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解题步骤 4.1

Multiply each element of $R_{2}$ by $\frac{1}{0.008}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 0.15 & 0.35 & 1.5 \\ \frac{0}{0.008} & \frac{0.008}{0.008} & \frac{- 0.028}{0.008} & \frac{- 0.02}{0.008} \\ 0 & - 0.023 & - 0.007 & 0.67 \end{array}]$

解题步骤 4.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 0.15 & 0.35 & 1.5 \\ 0 & 1 & - 3.5 & - 2.5 \\ 0 & - 0.023 & - 0.007 & 0.67 \end{array}]$

解题步骤 5

Perform the row operation $R_{3} = R_{3} + 0.023 R_{2}$ to make the entry at $3, 2$ a $0$ .

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解题步骤 5.1

Perform the row operation $R_{3} = R_{3} + 0.023 R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & 0.15 & 0.35 & 1.5 \\ 0 & 1 & - 3.5 & - 2.5 \\ 0 + 0.023 \cdot 0 & - 0.023 + 0.023 \cdot 1 & - 0.007 + 0.023 \cdot - 3.5 & 0.67 + 0.023 \cdot - 2.5 \end{array}]$

解题步骤 5.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 0.15 & 0.35 & 1.5 \\ 0 & 1 & - 3.5 & - 2.5 \\ 0 & 0 & - 0.0875 & 0.6125 \end{array}]$

解题步骤 6

Multiply each element of $R_{3}$ by $\frac{1}{- 0.0875}$ to make the entry at $3, 3$ a $1$ .

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解题步骤 6.1

Multiply each element of $R_{3}$ by $\frac{1}{- 0.0875}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 0.15 & 0.35 & 1.5 \\ 0 & 1 & - 3.5 & - 2.5 \\ \frac{0}{- 0.0875} & \frac{0}{- 0.0875} & \frac{- 0.0875}{- 0.0875} & \frac{0.6125}{- 0.0875} \end{array}]$

解题步骤 6.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 0.15 & 0.35 & 1.5 \\ 0 & 1 & - 3.5 & - 2.5 \\ 0 & 0 & 1 & - 7 \end{array}]$

解题步骤 7

Perform the row operation $R_{2} = R_{2} + 3.5 R_{3}$ to make the entry at $2, 3$ a $0$ .

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解题步骤 7.1

Perform the row operation $R_{2} = R_{2} + 3.5 R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 0.15 & 0.35 & 1.5 \\ 0 + 3.5 \cdot 0 & 1 + 3.5 \cdot 0 & - 3.5 + 3.5 \cdot 1 & - 2.5 + 3.5 \cdot - 7 \\ 0 & 0 & 1 & - 7 \end{array}]$

解题步骤 7.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 0.15 & 0.35 & 1.5 \\ 0 & 1 & 0 & - 27 \\ 0 & 0 & 1 & - 7 \end{array}]$

解题步骤 8

Perform the row operation $R_{1} = R_{1} - 0.35 R_{3}$ to make the entry at $1, 3$ a $0$ .

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解题步骤 8.1

Perform the row operation $R_{1} = R_{1} - 0.35 R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 - 0.35 \cdot 0 & 0.15 - 0.35 \cdot 0 & 0.35 - 0.35 \cdot 1 & 1.5 - 0.35 \cdot - 7 \\ 0 & 1 & 0 & - 27 \\ 0 & 0 & 1 & - 7 \end{array}]$

解题步骤 8.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & 0.15 & 0 & 3.95 \\ 0 & 1 & 0 & - 27 \\ 0 & 0 & 1 & - 7 \end{array}]$

解题步骤 9

Perform the row operation $R_{1} = R_{1} - 0.15 R_{2}$ to make the entry at $1, 2$ a $0$ .

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解题步骤 9.1

Perform the row operation $R_{1} = R_{1} - 0.15 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - 0.15 \cdot 0 & 0.15 - 0.15 \cdot 1 & 0 - 0.15 \cdot 0 & 3.95 - 0.15 \cdot - 27 \\ 0 & 1 & 0 & - 27 \\ 0 & 0 & 1 & - 7 \end{array}]$

解题步骤 9.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & 0 & 0 & 8 \\ 0 & 1 & 0 & - 27 \\ 0 & 0 & 1 & - 7 \end{array}]$

有限数学 示例

有限数学示例