Matematika Berhingga Contoh

$x - 3 y = - 5$ , $2 x - 6 y = - 3$

Langkah 1

Write the system as a matrix.

$[\begin{array}{c} 1 & - 3 & - 5 \\ 2 & - 6 & - 3 \end{array}]$

Langkah 2

Tentukan bentuk eselon baris yang dikurangi.

Ketuk untuk lebih banyak langkah...

Langkah 2.1

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

Ketuk untuk lebih banyak langkah...

Langkah 2.1.1

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

$[\begin{array}{c} 1 & - 3 & - 5 \\ 2 - 2 \cdot 1 & - 6 - 2 \cdot - 3 & - 3 - 2 \cdot - 5 \end{array}]$

Langkah 2.1.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & - 3 & - 5 \\ 0 & 0 & 7 \end{array}]$

Langkah 2.2

Multiply each element of $R_{2}$ by $\frac{1}{7}$ to make the entry at $2, 3$ a $1$ .

Ketuk untuk lebih banyak langkah...

Langkah 2.2.1

Multiply each element of $R_{2}$ by $\frac{1}{7}$ to make the entry at $2, 3$ a $1$ .

$[\begin{array}{c} 1 & - 3 & - 5 \\ \frac{0}{7} & \frac{0}{7} & \frac{7}{7} \end{array}]$

Langkah 2.2.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & - 3 & - 5 \\ 0 & 0 & 1 \end{array}]$

Langkah 2.3

Perform the row operation $R_{1} = R_{1} + 5 R_{2}$ to make the entry at $1, 3$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 2.3.1

Perform the row operation $R_{1} = R_{1} + 5 R_{2}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 + 5 \cdot 0 & - 3 + 5 \cdot 0 & - 5 + 5 \cdot 1 \\ 0 & 0 & 1 \end{array}]$

Langkah 2.3.2

Sederhanakan $R_{1}$ .

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

Langkah 3

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

$x - 3 y = 0$

$0 = 1$

Langkah 4

The system is inconsistent so there is no solution.

$Tidak ada penyelesaian$