Đại số tuyến tính Ví dụ

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2.04 a & - 1 b & 0 d & 0 g - 1 a & 2.04 b & - 1 d & 0 g 0 a & - 1 b & 2.04 d & - 1 g 0 a & 0 b & - 1 d & 2.04 g \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 40.8 0.8 0.8 200.8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

$[\begin{array}{c} 2.04 a & - 1 b & 0 d & 0 g \\ - 1 a & 2.04 b & - 1 d & 0 g \\ 0 a & - 1 b & 2.04 d & - 1 g \\ 0 a & 0 b & - 1 d & 2.04 g \end{array}] - [\begin{array}{c} 40.8 \\ 0.8 \\ 0.8 \\ 200.8 \end{array}]$

Bước 1

Viết lại

- 1 b

$- 1 b$ ở dạng

- b

$- b$ .

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2.04 a & - b & 0 d & 0 g - 1 a & 2.04 b & - 1 d & 0 g 0 a & - 1 b & 2.04 d & - 1 g 0 a & 0 b & - 1 d & 2.04 g \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 40.8 0.8 0.8 200.8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

$[\begin{array}{c} 2.04 a & - b & 0 d & 0 g \\ - 1 a & 2.04 b & - 1 d & 0 g \\ 0 a & - 1 b & 2.04 d & - 1 g \\ 0 a & 0 b & - 1 d & 2.04 g \end{array}] - [\begin{array}{c} 40.8 \\ 0.8 \\ 0.8 \\ 200.8 \end{array}]$

Bước 2

Nhân

0

$0$ với

d

$d$ .

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2.04 a & - b & 0 & 0 g - 1 a & 2.04 b & - 1 d & 0 g 0 a & - 1 b & 2.04 d & - 1 g 0 a & 0 b & - 1 d & 2.04 g \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 40.8 0.8 0.8 200.8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

$[\begin{array}{c} 2.04 a & - b & 0 & 0 g \\ - 1 a & 2.04 b & - 1 d & 0 g \\ 0 a & - 1 b & 2.04 d & - 1 g \\ 0 a & 0 b & - 1 d & 2.04 g \end{array}] - [\begin{array}{c} 40.8 \\ 0.8 \\ 0.8 \\ 200.8 \end{array}]$

Bước 3

Nhân

0

$0$ với

g

$g$ .

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2.04 a & - b & 0 & 0 - 1 a & 2.04 b & - 1 d & 0 g 0 a & - 1 b & 2.04 d & - 1 g 0 a & 0 b & - 1 d & 2.04 g \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 40.8 0.8 0.8 200.8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

$[\begin{array}{c} 2.04 a & - b & 0 & 0 \\ - 1 a & 2.04 b & - 1 d & 0 g \\ 0 a & - 1 b & 2.04 d & - 1 g \\ 0 a & 0 b & - 1 d & 2.04 g \end{array}] - [\begin{array}{c} 40.8 \\ 0.8 \\ 0.8 \\ 200.8 \end{array}]$

Bước 4

Viết lại

- 1 a

$- 1 a$ ở dạng

- a

$- a$ .

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2.04 a & - b & 0 & 0 - a & 2.04 b & - 1 d & 0 g 0 a & - 1 b & 2.04 d & - 1 g 0 a & 0 b & - 1 d & 2.04 g \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 40.8 0.8 0.8 200.8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

$[\begin{array}{c} 2.04 a & - b & 0 & 0 \\ - a & 2.04 b & - 1 d & 0 g \\ 0 a & - 1 b & 2.04 d & - 1 g \\ 0 a & 0 b & - 1 d & 2.04 g \end{array}] - [\begin{array}{c} 40.8 \\ 0.8 \\ 0.8 \\ 200.8 \end{array}]$

Bước 5

Viết lại

- 1 d

$- 1 d$ ở dạng

- d

$- d$ .

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2.04 a & - b & 0 & 0 - a & 2.04 b & - d & 0 g 0 a & - 1 b & 2.04 d & - 1 g 0 a & 0 b & - 1 d & 2.04 g \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 40.8 0.8 0.8 200.8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

$[\begin{array}{c} 2.04 a & - b & 0 & 0 \\ - a & 2.04 b & - d & 0 g \\ 0 a & - 1 b & 2.04 d & - 1 g \\ 0 a & 0 b & - 1 d & 2.04 g \end{array}] - [\begin{array}{c} 40.8 \\ 0.8 \\ 0.8 \\ 200.8 \end{array}]$

Bước 6

Nhân

0

$0$ với

g

$g$ .

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2.04 a & - b & 0 & 0 - a & 2.04 b & - d & 0 0 a & - 1 b & 2.04 d & - 1 g 0 a & 0 b & - 1 d & 2.04 g \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 40.8 0.8 0.8 200.8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

$[\begin{array}{c} 2.04 a & - b & 0 & 0 \\ - a & 2.04 b & - d & 0 \\ 0 a & - 1 b & 2.04 d & - 1 g \\ 0 a & 0 b & - 1 d & 2.04 g \end{array}] - [\begin{array}{c} 40.8 \\ 0.8 \\ 0.8 \\ 200.8 \end{array}]$

Bước 7

Nhân

0

$0$ với

a

$a$ .

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2.04 a & - b & 0 & 0 - a & 2.04 b & - d & 0 0 & - 1 b & 2.04 d & - 1 g 0 a & 0 b & - 1 d & 2.04 g \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 40.8 0.8 0.8 200.8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

$[\begin{array}{c} 2.04 a & - b & 0 & 0 \\ - a & 2.04 b & - d & 0 \\ 0 & - 1 b & 2.04 d & - 1 g \\ 0 a & 0 b & - 1 d & 2.04 g \end{array}] - [\begin{array}{c} 40.8 \\ 0.8 \\ 0.8 \\ 200.8 \end{array}]$

Bước 8

Viết lại

- 1 b

$- 1 b$ ở dạng

- b

$- b$ .

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2.04 a & - b & 0 & 0 - a & 2.04 b & - d & 0 0 & - b & 2.04 d & - 1 g 0 a & 0 b & - 1 d & 2.04 g \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 40.8 0.8 0.8 200.8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

$[\begin{array}{c} 2.04 a & - b & 0 & 0 \\ - a & 2.04 b & - d & 0 \\ 0 & - b & 2.04 d & - 1 g \\ 0 a & 0 b & - 1 d & 2.04 g \end{array}] - [\begin{array}{c} 40.8 \\ 0.8 \\ 0.8 \\ 200.8 \end{array}]$

Bước 9

Viết lại

- 1 g

$- 1 g$ ở dạng

- g

$- g$ .

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2.04 a & - b & 0 & 0 - a & 2.04 b & - d & 0 0 & - b & 2.04 d & - g 0 a & 0 b & - 1 d & 2.04 g \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 40.8 0.8 0.8 200.8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

$[\begin{array}{c} 2.04 a & - b & 0 & 0 \\ - a & 2.04 b & - d & 0 \\ 0 & - b & 2.04 d & - g \\ 0 a & 0 b & - 1 d & 2.04 g \end{array}] - [\begin{array}{c} 40.8 \\ 0.8 \\ 0.8 \\ 200.8 \end{array}]$

Bước 10

Nhân

0

$0$ với

a

$a$ .

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2.04 a & - b & 0 & 0 - a & 2.04 b & - d & 0 0 & - b & 2.04 d & - g 0 & 0 b & - 1 d & 2.04 g \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 40.8 0.8 0.8 200.8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

$[\begin{array}{c} 2.04 a & - b & 0 & 0 \\ - a & 2.04 b & - d & 0 \\ 0 & - b & 2.04 d & - g \\ 0 & 0 b & - 1 d & 2.04 g \end{array}] - [\begin{array}{c} 40.8 \\ 0.8 \\ 0.8 \\ 200.8 \end{array}]$

Bước 11

Nhân

0

$0$ với

b

$b$ .

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2.04 a & - b & 0 & 0 - a & 2.04 b & - d & 0 0 & - b & 2.04 d & - g 0 & 0 & - 1 d & 2.04 g \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 40.8 0.8 0.8 200.8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

$[\begin{array}{c} 2.04 a & - b & 0 & 0 \\ - a & 2.04 b & - d & 0 \\ 0 & - b & 2.04 d & - g \\ 0 & 0 & - 1 d & 2.04 g \end{array}] - [\begin{array}{c} 40.8 \\ 0.8 \\ 0.8 \\ 200.8 \end{array}]$

Bước 12

Viết lại

- 1 d

$- 1 d$ ở dạng

- d

$- d$ .

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2.04 a & - b & 0 & 0 - a & 2.04 b & - d & 0 0 & - b & 2.04 d & - g 0 & 0 & - d & 2.04 g \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 40.8 0.8 0.8 200.8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

$[\begin{array}{c} 2.04 a & - b & 0 & 0 \\ - a & 2.04 b & - d & 0 \\ 0 & - b & 2.04 d & - g \\ 0 & 0 & - d & 2.04 g \end{array}] - [\begin{array}{c} 40.8 \\ 0.8 \\ 0.8 \\ 200.8 \end{array}]$