Algebra lineare Esempi

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

Passaggio 1

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

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Passaggio 1.1

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

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

Passaggio 1.2

Semplifica $R_{2}$ .

$[\begin{array}{c} 1 & 2 & 7 \\ 0 & - 3 & - 6 \end{array}]$

Passaggio 2

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

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Passaggio 2.1

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

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

Passaggio 2.2

Semplifica $R_{2}$ .

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

Passaggio 3

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

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Passaggio 3.1

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

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

Passaggio 3.2

Semplifica $R_{1}$ .

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