Álgebra linear Exemplos

⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \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} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

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

Etapa 1

Reescreva

- 1 b

$- 1 b$ como

- 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} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

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

Etapa 2

Multiplique

0

$0$ por

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} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

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

Etapa 3

Multiplique

0

$0$ por

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} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

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

Etapa 4

Reescreva

- 1 a

$- 1 a$ como

- 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} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

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

Etapa 5

Reescreva

- 1 d

$- 1 d$ como

- 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} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

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

Etapa 6

Multiplique

0

$0$ por

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} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

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

Etapa 7

Multiplique

0

$0$ por

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} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

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

Etapa 8

Reescreva

$- 1 b$ como

$- b$ .

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

Etapa 9

Reescreva

$- 1 g$ como

$- g$ .

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

Etapa 10

Multiplique

$0$ por

$a$ .

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

Etapa 11

Multiplique

$0$ por

$b$ .

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

Etapa 12

Reescreva

$- 1 d$ como

$- d$ .

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