Álgebra lineal Ejemplos

$[\begin{array}{c} 1 & 3 & 9 & 0 \\ 0 & 1 & 8 & 3 \\ 0 & 0 & 0 & 0 \end{array}]$

Paso 1

Obtén la forma escalonada reducida por filas.

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Paso 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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Paso 1.1.1

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

$[\begin{array}{c} 1 - 3 \cdot 0 & 3 - 3 \cdot 1 & 9 - 3 \cdot 8 & 0 - 3 \cdot 3 \\ 0 & 1 & 8 & 3 \\ 0 & 0 & 0 & 0 \end{array}]$

Paso 1.1.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & 0 & - 15 & - 9 \\ 0 & 1 & 8 & 3 \\ 0 & 0 & 0 & 0 \end{array}]$

Paso 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 $2$