Álgebra Exemplos

$[\begin{array}{c} - 1 & 1 & 1 & - 1 \\ - 1 & 4 & - 11 & - 19 \\ 6 & - 5 & - 10 & 0 \end{array}]$

Etapa 1

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

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Etapa 1.1

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

$[\begin{array}{c} - - 1 & - 1 \cdot 1 & - 1 \cdot 1 & - - 1 \\ - 1 & 4 & - 11 & - 19 \\ 6 & - 5 & - 10 & 0 \end{array}]$

Etapa 1.2

Simplifique $R_{1}$ .

$[\begin{array}{c} 1 & - 1 & - 1 & 1 \\ - 1 & 4 & - 11 & - 19 \\ 6 & - 5 & - 10 & 0 \end{array}]$

Etapa 2

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

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Etapa 2.1

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

$[\begin{array}{c} 1 & - 1 & - 1 & 1 \\ - 1 + 1 \cdot 1 & 4 - 1 & - 11 - 1 & - 19 + 1 \cdot 1 \\ 6 & - 5 & - 10 & 0 \end{array}]$

Etapa 2.2

Simplifique $R_{2}$ .

$[\begin{array}{c} 1 & - 1 & - 1 & 1 \\ 0 & 3 & - 12 & - 18 \\ 6 & - 5 & - 10 & 0 \end{array}]$

Etapa 3

Perform the row operation $R_{3} = R_{3} - 6 R_{1}$ to make the entry at $3, 1$ a $0$ .

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Etapa 3.1

Perform the row operation $R_{3} = R_{3} - 6 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & - 1 & - 1 & 1 \\ 0 & 3 & - 12 & - 18 \\ 6 - 6 \cdot 1 & - 5 - 6 \cdot - 1 & - 10 - 6 \cdot - 1 & 0 - 6 \cdot 1 \end{array}]$

Etapa 3.2

Simplifique $R_{3}$ .

$[\begin{array}{c} 1 & - 1 & - 1 & 1 \\ 0 & 3 & - 12 & - 18 \\ 0 & 1 & - 4 & - 6 \end{array}]$

Etapa 4

Multiply each element of $R_{2}$ by $\frac{1}{3}$ to make the entry at $2, 2$ a $1$ .

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Etapa 4.1

Multiply each element of $R_{2}$ by $\frac{1}{3}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - 1 & - 1 & 1 \\ \frac{0}{3} & \frac{3}{3} & \frac{- 12}{3} & \frac{- 18}{3} \\ 0 & 1 & - 4 & - 6 \end{array}]$

Etapa 4.2

Simplifique $R_{2}$ .

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

Etapa 5

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

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Etapa 5.1

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

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

Etapa 5.2

Simplifique $R_{3}$ .

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

Etapa 6

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

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Etapa 6.1

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

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

Etapa 6.2

Simplifique $R_{1}$ .

$[\begin{array}{c} 1 & 0 & - 5 & - 5 \\ 0 & 1 & - 4 & - 6 \\ 0 & 0 & 0 & 0 \end{array}]$