代数示例

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

解题步骤 1

求行简化阶梯形矩阵。

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

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

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

化简 $R_{2}$ 。

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

Multiply each element of $R_{2}$ by $- 1$ to make the entry at $2, 3$ a $1$ .

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Multiply each element of $R_{2}$ by $- 1$ to make the entry at $2, 3$ a $1$ .

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

化简 $R_{2}$ 。

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

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

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

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

化简 $R_{1}$ 。

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

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 $a_{23}$

Pivot Columns: $1$ and $3$

解题步骤 3

The rank is the number of pivot columns.

$2$

代数 示例