线性代数示例

$[\begin{array}{c} 1 & 3 & 5 \\ 0 & 1 & \frac{1}{2} \end{array}]$

解题步骤 1

求行简化阶梯形矩阵。

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解题步骤 1.1

Perform the row operation $R_{1} = R_{1} - 3 R_{2}$ to make the entry at $1, 2$ a $0$ .

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解题步骤 1.1.1

Perform the row operation $R_{1} = R_{1} - 3 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - 3 \cdot 0 & 3 - 3 \cdot 1 & 5 - 3 (\frac{1}{2}) \\ 0 & 1 & \frac{1}{2} \end{array}]$

解题步骤 1.1.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & 0 & \frac{7}{2} \\ 0 & 1 & \frac{1}{2} \end{array}]$

解题步骤 2

The pivot positions are the locations with the leading $1$ in each row. The pivot columns are the columns that have a pivot position.

Pivot Positions: $a_{11}$ and $a_{22}$

Pivot Columns: $1$ and $2$

线性代数 示例