Đại số tuyến tính Ví dụ

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

Bước 1

Tìm dạng ma trận hàng bậc thang rút gọn.

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Bước 1.1

Perform the row operation

$R_{2} = R_{2} - R_{1}$ to make the entry at

$2, 1$ a

$0$ .

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Bước 1.1.1

Perform the row operation

$R_{2} = R_{2} - R_{1}$ to make the entry at

$2, 1$ a

$0$ .

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

Bước 1.1.2

Rút gọn

$R_{2}$ .

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

Bước 1.2

Perform the row operation

$R_{5} = R_{5} - R_{1}$ to make the entry at

$5, 1$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.2.1

Perform the row operation

$R_{5} = R_{5} - R_{1}$ to make the entry at

$5, 1$ a

$0$ .

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

Bước 1.2.2

Rút gọn

$R_{5}$ .

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

Bước 1.3

Perform the row operation

$R_{3} = R_{3} - R_{2}$ to make the entry at

$3, 2$ a

$0$ .

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Bước 1.3.1

Perform the row operation

$R_{3} = R_{3} - R_{2}$ to make the entry at

$3, 2$ a

$0$ .

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

Bước 1.3.2

Rút gọn

$R_{3}$ .

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

Bước 1.4

Perform the row operation

$R_{4} = R_{4} - R_{2}$ to make the entry at

$4, 2$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.4.1

Perform the row operation

$R_{4} = R_{4} - R_{2}$ to make the entry at

$4, 2$ a

$0$ .

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

Bước 1.4.2

Rút gọn

$R_{4}$ .

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

Bước 1.5

Perform the row operation

$R_{5} = R_{5} - R_{2}$ to make the entry at

$5, 2$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.5.1

Perform the row operation

$R_{5} = R_{5} - R_{2}$ to make the entry at

$5, 2$ a

$0$ .

$[\begin{array}{c} 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 1 & - 1 & - 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & - 1 & 2 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & - 1 & 3 & 2 & 0 & 0 & 0 & 0 & 0 \\ 0 - 0 & 1 - 1 & 0 - 1 & - 1 + 1 & - 1 + 1 & 0 - 0 & 0 - 0 & 0 - 0 & 0 - 0 & 0 - 0 \\ 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \end{array}]$

Bước 1.5.2

Rút gọn

$R_{5}$ .

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

Bước 1.6

Multiply each element of

$R_{3}$ by

$- 1$ to make the entry at

$3, 3$ a

$1$ .

Nhấp để xem thêm các bước...

Bước 1.6.1

Multiply each element of

$R_{3}$ by

$- 1$ to make the entry at

$3, 3$ a

$1$ .

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

Bước 1.6.2

Rút gọn

$R_{3}$ .

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

Bước 1.7

Perform the row operation

$R_{4} = R_{4} + R_{3}$ to make the entry at

$4, 3$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.7.1

Perform the row operation

$R_{4} = R_{4} + R_{3}$ to make the entry at

$4, 3$ a

$0$ .

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

Bước 1.7.2

Rút gọn

$R_{4}$ .

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

Bước 1.8

Perform the row operation

$R_{5} = R_{5} + R_{3}$ to make the entry at

$5, 3$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.8.1

Perform the row operation

$R_{5} = R_{5} + R_{3}$ to make the entry at

$5, 3$ a

$0$ .

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

Bước 1.8.2

Rút gọn

$R_{5}$ .

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

Bước 1.9

Perform the row operation

$R_{6} = R_{6} - R_{3}$ to make the entry at

$6, 3$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.9.1

Perform the row operation

$R_{6} = R_{6} - R_{3}$ to make the entry at

$6, 3$ a

$0$ .

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

Bước 1.9.2

Rút gọn

$R_{6}$ .

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

Bước 1.10

Perform the row operation

$R_{7} = R_{7} - R_{3}$ to make the entry at

$7, 3$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.10.1

Perform the row operation

$R_{7} = R_{7} - R_{3}$ to make the entry at

$7, 3$ a

$0$ .

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

Bước 1.10.2

Rút gọn

$R_{7}$ .

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

Bước 1.11

Perform the row operation

$R_{5} = R_{5} + 2 R_{4}$ to make the entry at

$5, 4$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.11.1

Perform the row operation

$R_{5} = R_{5} + 2 R_{4}$ to make the entry at

$5, 4$ a

$0$ .

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

Bước 1.11.2

Rút gọn

$R_{5}$ .

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

Bước 1.12

Perform the row operation

$R_{6} = R_{6} - 2 R_{4}$ to make the entry at

$6, 4$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.12.1

Perform the row operation

$R_{6} = R_{6} - 2 R_{4}$ to make the entry at

$6, 4$ a

$0$ .

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

Bước 1.12.2

Rút gọn

$R_{6}$ .

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

Bước 1.13

Perform the row operation

$R_{7} = R_{7} - 2 R_{4}$ to make the entry at

$7, 4$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.13.1

Perform the row operation

$R_{7} = R_{7} - 2 R_{4}$ to make the entry at

$7, 4$ a

$0$ .

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

Bước 1.13.2

Rút gọn

$R_{7}$ .

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

Bước 1.14

Perform the row operation

$R_{7} = R_{7} + R_{5}$ to make the entry at

$7, 5$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.14.1

Perform the row operation

$R_{7} = R_{7} + R_{5}$ to make the entry at

$7, 5$ a

$0$ .

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

Bước 1.14.2

Rút gọn

$R_{7}$ .

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

Bước 1.15

Swap

$R_{8}$ with

$R_{6}$ to put a nonzero entry at

$6, 6$ .

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

Bước 1.16

Perform the row operation

$R_{9} = R_{9} - R_{6}$ to make the entry at

$9, 6$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.16.1

Perform the row operation

$R_{9} = R_{9} - R_{6}$ to make the entry at

$9, 6$ a

$0$ .

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

Bước 1.16.2

Rút gọn

$R_{9}$ .

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

Bước 1.17

Swap

$R_{9}$ with

$R_{7}$ to put a nonzero entry at

$7, 7$ .

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

Bước 1.18

Perform the row operation

$R_{10} = R_{10} - R_{7}$ to make the entry at

$10, 7$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.18.1

Perform the row operation

$R_{10} = R_{10} - R_{7}$ to make the entry at

$10, 7$ a

$0$ .

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

Bước 1.18.2

Rút gọn

$R_{10}$ .

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

Bước 1.19

Swap

$R_{10}$ with

$R_{8}$ to put a nonzero entry at

$8, 9$ .

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

Bước 1.20

Multiply each element of

$R_{8}$ by

$- 1$ to make the entry at

$8, 9$ a

$1$ .

Nhấp để xem thêm các bước...

Bước 1.20.1

Multiply each element of

$R_{8}$ by

$- 1$ to make the entry at

$8, 9$ a

$1$ .

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

Bước 1.20.2

Rút gọn

$R_{8}$ .

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

Bước 1.21

Perform the row operation

$R_{7} = R_{7} - R_{8}$ to make the entry at

$7, 9$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.21.1

Perform the row operation

$R_{7} = R_{7} - R_{8}$ to make the entry at

$7, 9$ a

$0$ .

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

Bước 1.21.2

Rút gọn

$R_{7}$ .

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

Bước 1.22

Perform the row operation

$R_{4} = R_{4} - R_{5}$ to make the entry at

$4, 5$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.22.1

Perform the row operation

$R_{4} = R_{4} - R_{5}$ to make the entry at

$4, 5$ a

$0$ .

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

Bước 1.22.2

Rút gọn

$R_{4}$ .

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

Bước 1.23

Perform the row operation

$R_{3} = R_{3} + R_{5}$ to make the entry at

$3, 5$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.23.1

Perform the row operation

$R_{3} = R_{3} + R_{5}$ to make the entry at

$3, 5$ a

$0$ .

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

Bước 1.23.2

Rút gọn

$R_{3}$ .

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

Bước 1.24

Perform the row operation

$R_{2} = R_{2} + R_{5}$ to make the entry at

$2, 5$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.24.1

Perform the row operation

$R_{2} = R_{2} + R_{5}$ to make the entry at

$2, 5$ a

$0$ .

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

Bước 1.24.2

Rút gọn

$R_{2}$ .

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

Bước 1.25

Perform the row operation

$R_{1} = R_{1} - R_{5}$ to make the entry at

$1, 5$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.25.1

Perform the row operation

$R_{1} = R_{1} - R_{5}$ to make the entry at

$1, 5$ a

$0$ .

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

Bước 1.25.2

Rút gọn

$R_{1}$ .

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

Bước 1.26

Perform the row operation

$R_{3} = R_{3} + 2 R_{4}$ to make the entry at

$3, 4$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.26.1

Perform the row operation

$R_{3} = R_{3} + 2 R_{4}$ to make the entry at

$3, 4$ a

$0$ .

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

Bước 1.26.2

Rút gọn

$R_{3}$ .

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

Bước 1.27

Perform the row operation

$R_{2} = R_{2} + R_{4}$ to make the entry at

$2, 4$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.27.1

Perform the row operation

$R_{2} = R_{2} + R_{4}$ to make the entry at

$2, 4$ a

$0$ .

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

Bước 1.27.2

Rút gọn

$R_{2}$ .

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

Bước 1.28

Perform the row operation

$R_{1} = R_{1} - R_{4}$ to make the entry at

$1, 4$ a

$0$ .

Nhấp để xem thêm các bước...

Bước 1.28.1

Perform the row operation

$R_{1} = R_{1} - R_{4}$ to make the entry at

$1, 4$ a

$0$ .

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

Bước 1.28.2

Rút gọn

$R_{1}$ .

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

Bước 1.29

Perform the row operation

$R_{2} = R_{2} - R_{3}$ to make the entry at

$2, 3$ a

$0$ .

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Bước 1.29.1

Perform the row operation

$R_{2} = R_{2} - R_{3}$ to make the entry at

$2, 3$ a

$0$ .

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

Bước 1.29.2

Rút gọn

$R_{2}$ .

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

Bước 2

The pivot positions are the locations with the leading

$1$ in each row. The pivot columns are the columns that have a pivot position.

Pivot Positions:

$a_{11}, a_{22}, a_{33}, a_{44}, a_{55}, a_{66}, a_{77}, a_{89},$ and

$a_{910}$

Pivot Columns:

$1, 2, 3, 4, 5, 6, 7, 9,$ and

$10$

Bước 3

The rank is the number of pivot columns.

$9$