Toán hữu hạn Ví dụ

$[\begin{array}{c} 0.5 & 0.1 & 0.1 & 110 \\ 0.3 & 0.5 & 0.2 & 50 \\ 0.1 & 0.3 & 0.4 & 50 \end{array}]$

Bước 1

Multiply each element of $R_{1}$ by $\frac{1}{0.5}$ to make the entry at $1, 1$ a $1$ .

Nhấp để xem thêm các bước...

Bước 1.1

Multiply each element of $R_{1}$ by $\frac{1}{0.5}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{0.5}{0.5} & \frac{0.1}{0.5} & \frac{0.1}{0.5} & \frac{110}{0.5} \\ 0.3 & 0.5 & 0.2 & 50 \\ 0.1 & 0.3 & 0.4 & 50 \end{array}]$

Bước 1.2

Rút gọn $R_{1}$ .

$[\begin{array}{c} 1 & 0.2 & 0.2 & 220 \\ 0.3 & 0.5 & 0.2 & 50 \\ 0.1 & 0.3 & 0.4 & 50 \end{array}]$

Bước 2

Perform the row operation $R_{2} = R_{2} - 0.3 R_{1}$ to make the entry at $2, 1$ a $0$ .

Nhấp để xem thêm các bước...

Bước 2.1

Perform the row operation $R_{2} = R_{2} - 0.3 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 0.2 & 0.2 & 220 \\ 0.3 - 0.3 \cdot 1 & 0.5 - 0.3 \cdot 0.2 & 0.2 - 0.3 \cdot 0.2 & 50 - 0.3 \cdot 220 \\ 0.1 & 0.3 & 0.4 & 50 \end{array}]$

Bước 2.2

Rút gọn $R_{2}$ .

$[\begin{array}{c} 1 & 0.2 & 0.2 & 220 \\ 0 & 0.44 & 0.14 & - 16 \\ 0.1 & 0.3 & 0.4 & 50 \end{array}]$

Bước 3

Perform the row operation $R_{3} = R_{3} - 0.1 R_{1}$ to make the entry at $3, 1$ a $0$ .

Nhấp để xem thêm các bước...

Bước 3.1

Perform the row operation $R_{3} = R_{3} - 0.1 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 0.2 & 0.2 & 220 \\ 0 & 0.44 & 0.14 & - 16 \\ 0.1 - 0.1 \cdot 1 & 0.3 - 0.1 \cdot 0.2 & 0.4 - 0.1 \cdot 0.2 & 50 - 0.1 \cdot 220 \end{array}]$

Bước 3.2

Rút gọn $R_{3}$ .

$[\begin{array}{c} 1 & 0.2 & 0.2 & 220 \\ 0 & 0.44 & 0.14 & - 16 \\ 0 & 0.28 & 0.38 & 28 \end{array}]$

Bước 4

Multiply each element of $R_{2}$ by $\frac{1}{0.44}$ to make the entry at $2, 2$ a $1$ .

Nhấp để xem thêm các bước...

Bước 4.1

Multiply each element of $R_{2}$ by $\frac{1}{0.44}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 0.2 & 0.2 & 220 \\ \frac{0}{0.44} & \frac{0.44}{0.44} & \frac{0.14}{0.44} & \frac{- 16}{0.44} \\ 0 & 0.28 & 0.38 & 28 \end{array}]$

Bước 4.2

Rút gọn $R_{2}$ .

$[\begin{array}{c} 1 & 0.2 & 0.2 & 220 \\ 0 & 1 & 0.3\overline{18} & - 36.\overline{36} \\ 0 & 0.28 & 0.38 & 28 \end{array}]$

Bước 5

Perform the row operation $R_{3} = R_{3} - 0.28 R_{2}$ to make the entry at $3, 2$ a $0$ .

Nhấp để xem thêm các bước...

Bước 5.1

Perform the row operation $R_{3} = R_{3} - 0.28 R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & 0.2 & 0.2 & 220 \\ 0 & 1 & 0.3\overline{18} & - 36.\overline{36} \\ 0 - 0.28 \cdot 0 & 0.28 - 0.28 \cdot 1 & 0.38 - 0.28 \cdot 0.3\overline{18} & 28 - 0.28 \cdot - 36.\overline{36} \end{array}]$

Bước 5.2

Rút gọn $R_{3}$ .

$[\begin{array}{c} 1 & 0.2 & 0.2 & 220 \\ 0 & 1 & 0.3\overline{18} & - 36.\overline{36} \\ 0 & 0 & 0.2\overline{90} & 38.\overline{18} \end{array}]$

Bước 6

Multiply each element of $R_{3}$ by $\frac{1}{0.2\overline{90}}$ to make the entry at $3, 3$ a $1$ .

Nhấp để xem thêm các bước...

Bước 6.1

Multiply each element of $R_{3}$ by $\frac{1}{0.2\overline{90}}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 0.2 & 0.2 & 220 \\ 0 & 1 & 0.3\overline{18} & - 36.\overline{36} \\ \frac{0}{0.2\overline{90}} & \frac{0}{0.2\overline{90}} & \frac{0.2\overline{90}}{0.2\overline{90}} & \frac{38.\overline{18}}{0.2\overline{90}} \end{array}]$

Bước 6.2

Rút gọn $R_{3}$ .

$[\begin{array}{c} 1 & 0.2 & 0.2 & 220 \\ 0 & 1 & 0.3\overline{18} & - 36.\overline{36} \\ 0 & 0 & 1 & 131.25 \end{array}]$

Bước 7

Perform the row operation $R_{2} = R_{2} - 0.3\overline{18} R_{3}$ to make the entry at $2, 3$ a $0$ .

Nhấp để xem thêm các bước...

Bước 7.1

Perform the row operation $R_{2} = R_{2} - 0.3\overline{18} R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 0.2 & 0.2 & 220 \\ 0 - 0.3\overline{18} \cdot 0 & 1 - 0.3\overline{18} \cdot 0 & 0.3\overline{18} - 0.3\overline{18} \cdot 1 & - 36.\overline{36} - 0.3\overline{18} \cdot 131.25 \\ 0 & 0 & 1 & 131.25 \end{array}]$

Bước 7.2

Rút gọn $R_{2}$ .

$[\begin{array}{c} 1 & 0.2 & 0.2 & 220 \\ 0 & 1 & 0 & - 78.125 \\ 0 & 0 & 1 & 131.25 \end{array}]$

Bước 8

Perform the row operation $R_{1} = R_{1} - 0.2 R_{3}$ to make the entry at $1, 3$ a $0$ .

Nhấp để xem thêm các bước...

Bước 8.1

Perform the row operation $R_{1} = R_{1} - 0.2 R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 - 0.2 \cdot 0 & 0.2 - 0.2 \cdot 0 & 0.2 - 0.2 \cdot 1 & 220 - 0.2 \cdot 131.25 \\ 0 & 1 & 0 & - 78.125 \\ 0 & 0 & 1 & 131.25 \end{array}]$

Bước 8.2

Rút gọn $R_{1}$ .

$[\begin{array}{c} 1 & 0.2 & 0 & 193.75 \\ 0 & 1 & 0 & - 78.125 \\ 0 & 0 & 1 & 131.25 \end{array}]$

Bước 9

Perform the row operation $R_{1} = R_{1} - 0.2 R_{2}$ to make the entry at $1, 2$ a $0$ .

Nhấp để xem thêm các bước...

Bước 9.1

Perform the row operation $R_{1} = R_{1} - 0.2 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - 0.2 \cdot 0 & 0.2 - 0.2 \cdot 1 & 0 - 0.2 \cdot 0 & 193.75 - 0.2 \cdot - 78.125 \\ 0 & 1 & 0 & - 78.125 \\ 0 & 0 & 1 & 131.25 \end{array}]$

Bước 9.2

Rút gọn $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & 209.375 \\ 0 & 1 & 0 & - 78.125 \\ 0 & 0 & 1 & 131.25 \end{array}]$