Lineare Algebra Beispiele

u = [\begin{matrix} 2 i & - 3 j & k \end{matrix}]

$u = [\begin{array}{c} 2 i & - 3 j & k \end{array}]$

Schritt 1

Ermittele die normierte Zeilenstufenform.

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Schritt 1.1

Multiply each element of

R_{1}

$R_{1}$ by

\frac{1}{2 i}

$\frac{1}{2 i}$ to make the entry at

1, 1

$1, 1$ a

1

$1$ .

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Schritt 1.1.1

Multiply each element of

R_{1}

$R_{1}$ by

\frac{1}{2 i}

$\frac{1}{2 i}$ to make the entry at

1, 1

$1, 1$ a

1

$1$ .

[\begin{matrix} \frac{2 i}{2 i} & \frac{- 3 j}{2 i} & \frac{k}{2 i} \end{matrix}]

$[\begin{array}{c} \frac{2 i}{2 i} & \frac{- 3 j}{2 i} & \frac{k}{2 i} \end{array}]$

Schritt 1.1.2

Vereinfache

R_{1}

$R_{1}$ .

[\begin{matrix} 1 & \frac{3 j i}{2} & - \frac{k i}{2} \end{matrix}]

$[\begin{array}{c} 1 & \frac{3 j i}{2} & - \frac{k i}{2} \end{array}]$

[\begin{matrix} 1 & \frac{3 j i}{2} & - \frac{k i}{2} \end{matrix}]

$[\begin{array}{c} 1 & \frac{3 j i}{2} & - \frac{k i}{2} \end{array}]$

[\begin{matrix} 1 & \frac{3 j i}{2} & - \frac{k i}{2} \end{matrix}]

$[\begin{array}{c} 1 & \frac{3 j i}{2} & - \frac{k i}{2} \end{array}]$

Schritt 2

The pivot positions are the locations with the leading

1

$1$ in each row. The pivot columns are the columns that have a pivot position.

Pivot Positions:

u_{11}

$u_{11}$

Pivot Columns:

1

$1$