Matemática discreta Ejemplos

$[\begin{array}{c} 6 & 7 & 50 \\ 3 & 8 & 51 \end{array}]$

Paso 1

Obtén la forma escalonada reducida por filas.

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Paso 1.1

Multiply each element of $R_{1}$ by $\frac{1}{6}$ to make the entry at $1, 1$ a $1$ .

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Paso 1.1.1

Multiply each element of $R_{1}$ by $\frac{1}{6}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{6}{6} & \frac{7}{6} & \frac{50}{6} \\ 3 & 8 & 51 \end{array}]$

Paso 1.1.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & \frac{7}{6} & \frac{25}{3} \\ 3 & 8 & 51 \end{array}]$

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 $0$ .

$[\begin{array}{c} 1 & \frac{7}{6} & \frac{25}{3} \\ 3 - 3 \cdot 1 & 8 - 3 (\frac{7}{6}) & 51 - 3 (\frac{25}{3}) \end{array}]$

Paso 1.2.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & \frac{7}{6} & \frac{25}{3} \\ 0 & \frac{9}{2} & 26 \end{array}]$

Paso 1.3

Multiply each element of $R_{2}$ by $\frac{2}{9}$ to make the entry at $2, 2$ a $1$ .

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Paso 1.3.1

Multiply each element of $R_{2}$ by $\frac{2}{9}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{7}{6} & \frac{25}{3} \\ \frac{2}{9} \cdot 0 & \frac{2}{9} \cdot \frac{9}{2} & \frac{2}{9} \cdot 26 \end{array}]$

Paso 1.3.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & \frac{7}{6} & \frac{25}{3} \\ 0 & 1 & \frac{52}{9} \end{array}]$

Paso 1.4

Perform the row operation $R_{1} = R_{1} - \frac{7}{6} R_{2}$ to make the entry at $1, 2$ a $0$ .

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Paso 1.4.1

Perform the row operation $R_{1} = R_{1} - \frac{7}{6} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{7}{6} \cdot 0 & \frac{7}{6} - \frac{7}{6} \cdot 1 & \frac{25}{3} - \frac{7}{6} \cdot \frac{52}{9} \\ 0 & 1 & \frac{52}{9} \end{array}]$

Paso 1.4.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & 0 & \frac{43}{27} \\ 0 & 1 & \frac{52}{9} \end{array}]$

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 $2$