線形代数例

$[\begin{array}{c} 1 \\ - 2 \end{array}]$

ステップ 1

Nullity is the dimension of the null space, which is the same as the number of free variables in the system after row reducing. The free variables are the columns without pivot positions.

ステップ 2

縮小行の階段形を求めます。

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ステップ 2.1

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

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ステップ 2.1.1

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

$[\begin{array}{c} 1 \\ - 2 + 2 \cdot 1 \end{array}]$

ステップ 2.1.2

$R_{2}$ を簡約します。

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

ステップ 3

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: $a_{11}$

Pivot Columns: $1$

ステップ 4

The nullity is the number of columns without a pivot position in the row reduced matrix.

$0$

線形代数 例

線形代数例