Algebra lineare Esempi

$[\begin{array}{c} 1 & 3 & 0 & - 4 \\ 2 & 6 & 0 & - 8 \end{array}]$

Passaggio 1

Trova la forma ridotta a scala per righe di Echelon.

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Passaggio 1.1

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

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Passaggio 1.1.1

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

$[\begin{array}{c} 1 & 3 & 0 & - 4 \\ 2 - 2 \cdot 1 & 6 - 2 \cdot 3 & 0 - 2 \cdot 0 & - 8 - 2 \cdot - 4 \end{array}]$

Passaggio 1.1.2

Semplifica $R_{2}$ .

$[\begin{array}{c} 1 & 3 & 0 & - 4 \\ 0 & 0 & 0 & 0 \end{array}]$

Passaggio 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: $a_{11}$

Pivot Columns: $1$