Toán hữu hạn Ví dụ

$4 m + 3 n = 26$ , $3 m + 7 n = 29$

Bước 1

Write the system as a matrix.

$[\begin{array}{c} 4 & 3 & 26 \\ 3 & 7 & 29 \end{array}]$

Bước 2

Tìm dạng ma trận hàng bậc thang rút gọn.

Nhấp để xem thêm các bước...

Bước 2.1

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

Nhấp để xem thêm các bước...

Bước 2.1.1

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

$[\begin{array}{c} \frac{4}{4} & \frac{3}{4} & \frac{26}{4} \\ 3 & 7 & 29 \end{array}]$

Bước 2.1.2

Rút gọn $R_{1}$ .

$[\begin{array}{c} 1 & \frac{3}{4} & \frac{13}{2} \\ 3 & 7 & 29 \end{array}]$

Bước 2.2

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

Nhấp để xem thêm các bước...

Bước 2.2.1

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

$[\begin{array}{c} 1 & \frac{3}{4} & \frac{13}{2} \\ 3 - 3 \cdot 1 & 7 - 3 (\frac{3}{4}) & 29 - 3 (\frac{13}{2}) \end{array}]$

Bước 2.2.2

Rút gọn $R_{2}$ .

$[\begin{array}{c} 1 & \frac{3}{4} & \frac{13}{2} \\ 0 & \frac{19}{4} & \frac{19}{2} \end{array}]$

Bước 2.3

Multiply each element of $R_{2}$ by $\frac{4}{19}$ to make the entry at $2, 2$ a $1$ .

Nhấp để xem thêm các bước...

Bước 2.3.1

Multiply each element of $R_{2}$ by $\frac{4}{19}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{3}{4} & \frac{13}{2} \\ \frac{4}{19} \cdot 0 & \frac{4}{19} \cdot \frac{19}{4} & \frac{4}{19} \cdot \frac{19}{2} \end{array}]$

Bước 2.3.2

Rút gọn $R_{2}$ .

$[\begin{array}{c} 1 & \frac{3}{4} & \frac{13}{2} \\ 0 & 1 & 2 \end{array}]$

Bước 2.4

Perform the row operation $R_{1} = R_{1} - \frac{3}{4} R_{2}$ to make the entry at $1, 2$ a $0$ .

Nhấp để xem thêm các bước...

Bước 2.4.1

Perform the row operation $R_{1} = R_{1} - \frac{3}{4} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{3}{4} \cdot 0 & \frac{3}{4} - \frac{3}{4} \cdot 1 & \frac{13}{2} - \frac{3}{4} \cdot 2 \\ 0 & 1 & 2 \end{array}]$

Bước 2.4.2

Rút gọn $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 5 \\ 0 & 1 & 2 \end{array}]$

Bước 3

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

$m = 5$

$n = 2$

Bước 4

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

$(5, 2)$