Álgebra Ejemplos

$[\begin{array}{c} 1 & 2 & - 1 & 7 \\ 3 & 7 & - 5 & 14 \\ - 2 & - 1 & - 3 & 8 \end{array}]$

Paso 1

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 1.1

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

$[\begin{array}{c} 1 & 2 & - 1 & 7 \\ 3 - 3 \cdot 1 & 7 - 3 \cdot 2 & - 5 - 3 \cdot - 1 & 14 - 3 \cdot 7 \\ - 2 & - 1 & - 3 & 8 \end{array}]$

Paso 1.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & 2 & - 1 & 7 \\ 0 & 1 & - 2 & - 7 \\ - 2 & - 1 & - 3 & 8 \end{array}]$

Paso 2

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

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Paso 2.1

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

$[\begin{array}{c} 1 & 2 & - 1 & 7 \\ 0 & 1 & - 2 & - 7 \\ - 2 + 2 \cdot 1 & - 1 + 2 \cdot 2 & - 3 + 2 \cdot - 1 & 8 + 2 \cdot 7 \end{array}]$

Paso 2.2

Simplifica $R_{3}$ .

$[\begin{array}{c} 1 & 2 & - 1 & 7 \\ 0 & 1 & - 2 & - 7 \\ 0 & 3 & - 5 & 22 \end{array}]$

Paso 3

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

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Paso 3.1

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

$[\begin{array}{c} 1 & 2 & - 1 & 7 \\ 0 & 1 & - 2 & - 7 \\ 0 - 3 \cdot 0 & 3 - 3 \cdot 1 & - 5 - 3 \cdot - 2 & 22 - 3 \cdot - 7 \end{array}]$

Paso 3.2

Simplifica $R_{3}$ .

$[\begin{array}{c} 1 & 2 & - 1 & 7 \\ 0 & 1 & - 2 & - 7 \\ 0 & 0 & 1 & 43 \end{array}]$

Paso 4

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

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Paso 4.1

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

$[\begin{array}{c} 1 & 2 & - 1 & 7 \\ 0 + 2 \cdot 0 & 1 + 2 \cdot 0 & - 2 + 2 \cdot 1 & - 7 + 2 \cdot 43 \\ 0 & 0 & 1 & 43 \end{array}]$

Paso 4.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & 2 & - 1 & 7 \\ 0 & 1 & 0 & 79 \\ 0 & 0 & 1 & 43 \end{array}]$

Paso 5

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

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Paso 5.1

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

$[\begin{array}{c} 1 + 0 & 2 + 0 & - 1 + 1 \cdot 1 & 7 + 1 \cdot 43 \\ 0 & 1 & 0 & 79 \\ 0 & 0 & 1 & 43 \end{array}]$

Paso 5.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & 2 & 0 & 50 \\ 0 & 1 & 0 & 79 \\ 0 & 0 & 1 & 43 \end{array}]$

Paso 6

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

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Paso 6.1

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

$[\begin{array}{c} 1 - 2 \cdot 0 & 2 - 2 \cdot 1 & 0 - 2 \cdot 0 & 50 - 2 \cdot 79 \\ 0 & 1 & 0 & 79 \\ 0 & 0 & 1 & 43 \end{array}]$

Paso 6.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & - 108 \\ 0 & 1 & 0 & 79 \\ 0 & 0 & 1 & 43 \end{array}]$