Matematika Berhingga Contoh

$16 x + 8 y = 12000$ , $16 x + 8 y = 7200$

Langkah 1

Write the system as a matrix.

$[\begin{array}{c} 16 & 8 & 12000 \\ 16 & 8 & 7200 \end{array}]$

Langkah 2

Tentukan bentuk eselon baris yang dikurangi.

Ketuk untuk lebih banyak langkah...

Langkah 2.1

Multiply each element of $R_{1}$ by $\frac{1}{16}$ to make the entry at $1, 1$ a $1$ .

Ketuk untuk lebih banyak langkah...

Langkah 2.1.1

Multiply each element of $R_{1}$ by $\frac{1}{16}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{16}{16} & \frac{8}{16} & \frac{12000}{16} \\ 16 & 8 & 7200 \end{array}]$

Langkah 2.1.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & \frac{1}{2} & 750 \\ 16 & 8 & 7200 \end{array}]$

Langkah 2.2

Perform the row operation $R_{2} = R_{2} - 16 R_{1}$ to make the entry at $2, 1$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 2.2.1

Perform the row operation $R_{2} = R_{2} - 16 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{1}{2} & 750 \\ 16 - 16 \cdot 1 & 8 - 16 (\frac{1}{2}) & 7200 - 16 \cdot 750 \end{array}]$

Langkah 2.2.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & \frac{1}{2} & 750 \\ 0 & 0 & - 4800 \end{array}]$

Langkah 2.3

Multiply each element of $R_{2}$ by $- \frac{1}{4800}$ to make the entry at $2, 3$ a $1$ .

Ketuk untuk lebih banyak langkah...

Langkah 2.3.1

Multiply each element of $R_{2}$ by $- \frac{1}{4800}$ to make the entry at $2, 3$ a $1$ .

$[\begin{array}{c} 1 & \frac{1}{2} & 750 \\ - \frac{1}{4800} \cdot 0 & - \frac{1}{4800} \cdot 0 & - \frac{1}{4800} \cdot - 4800 \end{array}]$

Langkah 2.3.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & \frac{1}{2} & 750 \\ 0 & 0 & 1 \end{array}]$

Langkah 2.4

Perform the row operation $R_{1} = R_{1} - 750 R_{2}$ to make the entry at $1, 3$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 2.4.1

Perform the row operation $R_{1} = R_{1} - 750 R_{2}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 - 750 \cdot 0 & \frac{1}{2} - 750 \cdot 0 & 750 - 750 \cdot 1 \\ 0 & 0 & 1 \end{array}]$

Langkah 2.4.2

Sederhanakan $R_{1}$ .

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

Langkah 3

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

$x + \frac{1}{2} y = 0$

$0 = 1$

Langkah 4

The system is inconsistent so there is no solution.

$Tidak ada penyelesaian$