Algebra lineare Esempi

$[\begin{array}{c} 4 & 252 \\ 4 & - 4 \end{array}]$

Passaggio 1

Multiply each element of $R_{1}$ by $\frac{1}{4}$ to make the entry at $1, 1$ a $1$ .

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Passaggio 1.1

Multiply each element of $R_{1}$ by $\frac{1}{4}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{4}{4} & \frac{252}{4} \\ 4 & - 4 \end{array}]$

Passaggio 1.2

Semplifica $R_{1}$ .

$[\begin{array}{c} 1 & 63 \\ 4 & - 4 \end{array}]$

Passaggio 2

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Passaggio 2.1

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 63 \\ 4 - 4 \cdot 1 & - 4 - 4 \cdot 63 \end{array}]$

Passaggio 2.2

Semplifica $R_{2}$ .

$[\begin{array}{c} 1 & 63 \\ 0 & - 256 \end{array}]$

Passaggio 3

Multiply each element of $R_{2}$ by $- \frac{1}{256}$ to make the entry at $2, 2$ a $1$ .

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Passaggio 3.1

Multiply each element of $R_{2}$ by $- \frac{1}{256}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 63 \\ - \frac{1}{256} \cdot 0 & - \frac{1}{256} \cdot - 256 \end{array}]$

Passaggio 3.2

Semplifica $R_{2}$ .

$[\begin{array}{c} 1 & 63 \\ 0 & 1 \end{array}]$

Passaggio 4

Perform the row operation $R_{1} = R_{1} - 63 R_{2}$ to make the entry at $1, 2$ a $0$ .

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Passaggio 4.1

Perform the row operation $R_{1} = R_{1} - 63 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - 63 \cdot 0 & 63 - 63 \cdot 1 \\ 0 & 1 \end{array}]$

Passaggio 4.2

Semplifica $R_{1}$ .

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