Matematika Berhingga Contoh

$x + y = 7$ , $3 x - y = 9$

Langkah 1

Write the system as a matrix.

$[\begin{array}{c} 1 & 1 & 7 \\ 3 & - 1 & 9 \end{array}]$

Langkah 2

Tentukan bentuk eselon baris yang dikurangi.

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Langkah 2.1

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

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Langkah 2.1.1

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

$[\begin{array}{c} 1 & 1 & 7 \\ 3 - 3 \cdot 1 & - 1 - 3 \cdot 1 & 9 - 3 \cdot 7 \end{array}]$

Langkah 2.1.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & 1 & 7 \\ 0 & - 4 & - 12 \end{array}]$

Langkah 2.2

Multiply each element of $R_{2}$ by $- \frac{1}{4}$ to make the entry at $2, 2$ a $1$ .

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Langkah 2.2.1

Multiply each element of $R_{2}$ by $- \frac{1}{4}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 1 & 7 \\ - \frac{1}{4} \cdot 0 & - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot - 12 \end{array}]$

Langkah 2.2.2

Sederhanakan $R_{2}$ .

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

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 $0$ .

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

Langkah 2.3.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 4 \\ 0 & 1 & 3 \end{array}]$

Langkah 3

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

$x = 4$

$y = 3$

Langkah 4

The solution is the set of ordered pairs that make the system true.

$(4, 3)$