Matemática discreta Ejemplos

$[\begin{array}{c} 2 & 1 & 7 \\ - 3 & - 2 & - 1 \end{array}]$

Paso 1

Obtén la forma escalonada reducida por filas.

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Paso 1.1

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

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Paso 1.1.1

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

$[\begin{array}{c} \frac{2}{2} & \frac{1}{2} & \frac{7}{2} \\ - 3 & - 2 & - 1 \end{array}]$

Paso 1.1.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & \frac{1}{2} & \frac{7}{2} \\ - 3 & - 2 & - 1 \end{array}]$

Paso 1.2

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

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Paso 1.2.1

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

$[\begin{array}{c} 1 & \frac{1}{2} & \frac{7}{2} \\ - 3 + 3 \cdot 1 & - 2 + 3 (\frac{1}{2}) & - 1 + 3 (\frac{7}{2}) \end{array}]$

Paso 1.2.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & \frac{1}{2} & \frac{7}{2} \\ 0 & - \frac{1}{2} & \frac{19}{2} \end{array}]$

Paso 1.3

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

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Paso 1.3.1

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

$[\begin{array}{c} 1 & \frac{1}{2} & \frac{7}{2} \\ - 2 \cdot 0 & - 2 (- \frac{1}{2}) & - 2 (\frac{19}{2}) \end{array}]$

Paso 1.3.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & \frac{1}{2} & \frac{7}{2} \\ 0 & 1 & - 19 \end{array}]$

Paso 1.4

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

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Paso 1.4.1

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

$[\begin{array}{c} 1 - \frac{1}{2} \cdot 0 & \frac{1}{2} - \frac{1}{2} \cdot 1 & \frac{7}{2} - \frac{1}{2} \cdot - 19 \\ 0 & 1 & - 19 \end{array}]$

Paso 1.4.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 13 \\ 0 & 1 & - 19 \end{array}]$

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 $2$