Algebra lineare Esempi

$[\begin{array}{c} 1000 & 5000 & 10000 & 99000 \\ 2 & 1 & 0 & 26 \end{array}]$

Passaggio 1

Multiply each element of $R_{1}$ by $\frac{1}{1000}$ to make the entry at $1, 1$ a $1$ .

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Passaggio 1.1

Multiply each element of $R_{1}$ by $\frac{1}{1000}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{1000}{1000} & \frac{5000}{1000} & \frac{10000}{1000} & \frac{99000}{1000} \\ 2 & 1 & 0 & 26 \end{array}]$

Passaggio 1.2

Semplifica $R_{1}$ .

$[\begin{array}{c} 1 & 5 & 10 & 99 \\ 2 & 1 & 0 & 26 \end{array}]$

Passaggio 2

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 2.1

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

$[\begin{array}{c} 1 & 5 & 10 & 99 \\ 2 - 2 \cdot 1 & 1 - 2 \cdot 5 & 0 - 2 \cdot 10 & 26 - 2 \cdot 99 \end{array}]$

Passaggio 2.2

Semplifica $R_{2}$ .

$[\begin{array}{c} 1 & 5 & 10 & 99 \\ 0 & - 9 & - 20 & - 172 \end{array}]$

Passaggio 3

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

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Passaggio 3.1

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

$[\begin{array}{c} 1 & 5 & 10 & 99 \\ - \frac{1}{9} \cdot 0 & - \frac{1}{9} \cdot - 9 & - \frac{1}{9} \cdot - 20 & - \frac{1}{9} \cdot - 172 \end{array}]$

Passaggio 3.2

Semplifica $R_{2}$ .

$[\begin{array}{c} 1 & 5 & 10 & 99 \\ 0 & 1 & \frac{20}{9} & \frac{172}{9} \end{array}]$

Passaggio 4

Perform the row operation $R_{1} = R_{1} - 5 R_{2}$ to make the entry at $1, 2$ a $0$ .

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Passaggio 4.1

Perform the row operation $R_{1} = R_{1} - 5 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - 5 \cdot 0 & 5 - 5 \cdot 1 & 10 - 5 (\frac{20}{9}) & 99 - 5 (\frac{172}{9}) \\ 0 & 1 & \frac{20}{9} & \frac{172}{9} \end{array}]$

Passaggio 4.2

Semplifica $R_{1}$ .

$[\begin{array}{c} 1 & 0 & - \frac{10}{9} & \frac{31}{9} \\ 0 & 1 & \frac{20}{9} & \frac{172}{9} \end{array}]$