Aljabar Linear Contoh

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

Langkah 1

Write as an augmented matrix for $A x = 0$ .

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

Langkah 2

Tentukan bentuk eselon baris yang dikurangi.

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Langkah 2.1

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

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Langkah 2.1.1

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

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

Langkah 2.1.2

Sederhanakan $R_{2}$ .

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

Langkah 2.2

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

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Langkah 2.2.1

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

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

Langkah 2.2.2

Sederhanakan $R_{2}$ .

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

Langkah 2.3

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

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Langkah 2.3.1

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

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

Langkah 2.3.2

Sederhanakan $R_{1}$ .

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

Langkah 3

Use the result matrix to declare the final solution to the system of equations.

$x = 0$

$y = 0$

Langkah 4

Write a solution vector by solving in terms of the free variables in each row.

$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 0 \\ 0 \end{array}]$

Langkah 5

Write as a solution set.

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