Aljabar Linear Contoh

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

Langkah 1

Multiply each element of $R_{1}$ by $\frac{1}{7}$ to make the entry at $1, 1$ a $1$ .

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Langkah 1.1

Multiply each element of $R_{1}$ by $\frac{1}{7}$ to make the entry at $1, 1$ a $1$ .

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

Langkah 1.2

Sederhanakan $R_{1}$ .

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

Langkah 2

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

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Langkah 2.1

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

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

Langkah 2.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & \frac{2}{7} & \frac{1}{7} & 0 \\ 0 & \frac{43}{7} & - \frac{3}{7} & 1 \end{array}]$

Langkah 3

Multiply each element of $R_{2}$ by $\frac{7}{43}$ to make the entry at $2, 2$ a $1$ .

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Langkah 3.1

Multiply each element of $R_{2}$ by $\frac{7}{43}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{2}{7} & \frac{1}{7} & 0 \\ \frac{7}{43} \cdot 0 & \frac{7}{43} \cdot \frac{43}{7} & \frac{7}{43} (- \frac{3}{7}) & \frac{7}{43} \cdot 1 \end{array}]$

Langkah 3.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & \frac{2}{7} & \frac{1}{7} & 0 \\ 0 & 1 & - \frac{3}{43} & \frac{7}{43} \end{array}]$

Langkah 4

Perform the row operation $R_{1} = R_{1} - \frac{2}{7} R_{2}$ to make the entry at $1, 2$ a $0$ .

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Langkah 4.1

Perform the row operation $R_{1} = R_{1} - \frac{2}{7} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{2}{7} \cdot 0 & \frac{2}{7} - \frac{2}{7} \cdot 1 & \frac{1}{7} - \frac{2}{7} (- \frac{3}{43}) & 0 - \frac{2}{7} \cdot \frac{7}{43} \\ 0 & 1 & - \frac{3}{43} & \frac{7}{43} \end{array}]$

Langkah 4.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & 0 & \frac{7}{43} & - \frac{2}{43} \\ 0 & 1 & - \frac{3}{43} & \frac{7}{43} \end{array}]$