Question

Usando o processo de escalonamento , resolver o sistema :

( vou deixar aqui a resposta certa caso vocês precisem, me agradeçam depois ) ❤️

Answer 1

{ 3a + 3b + c - d = -2

{ a - b - c + d = 4

{ 2a - 2b + 5c + d = 6

{ -a + b - 2c + d = 0

Irei fazer por Cramer + Laplace, por escalonamento é chato demais lkk

$\sf D=\left[\begin{array}{ccc|c}3&3&1&-1\\1&-1&-1&1\\2&-2&5&1\\-1&1&-2&1\end{array}\right]$

-1*c14 + 1*c24 + 1*c34 + 1*c44

$\sf D=\left[\begin{array}{ccc|c}3&3&1&-1\\\cline{1-4}1&-1&-1&1\\2&-2&5&1\\-1&1&-2&1\end{array}\right]$

1*(-2)*(-2) + (-1)*5*(-1) + (-1)*2*1 - ( (-1)*(-2)*(-1) + 1*5*1 + (-2)*2*(-1) ) =

4 + 5 + (-2) - (-2) - 5 - 4 =

7 - 7 =

= 0

$\sf D=\left[\begin{array}{ccc|c}3&3&1&-1\\\cline{1-4}1&-1&-1&1\\\cline{1-4}2&-2&5&1\\-1&1&-2&1\end{array}\right]$

3*(-2)*(-2) + 3*5*(-1) + 1*2*1 - ( (-1)*(-2)*1 + 1*5*3 + (-2)*2*3 ) =

12 + (-15) + 2 - 2 - 15 - (-12) =

- 1 - 5 =

= -6

$\sf D=\left[\begin{array}{ccc|c}3&3&1&-1\\1&-1&-1&1\\\cline{1-4}2&-2&5&1\\\cline{1-4}-1&1&-2&1\end{array}\right]$

3*(-1)*(-2) + 3*(-1)*(-1) + 1*1*1 - ( (-1)*(-1)*1 + 1*(-1)*3 + (-2)*1*3 ) =

6 + 3 + 1 - 1 - (-3) - (-6) =

10 + 8 =

= 18

$\sf D=\left[\begin{array}{ccc|c}3&3&1&-1\\1&-1&-1&1\\2&-2&5&1\\\cline{1-4}-1&1&-2&1\end{array}\right]$

3*(-1)*5 + 3*(-1)*2 + 1*1*(-2) - ( 2*(-1)*1 + (-2)*(-1)*3 + 5*1*3 ) =

-15 + (-6) + (-2) - (-2) - 6 - 15 =

-23 - 19 =

= -42

-1*c14 + 1*c24 + 1*c34 + 1*c44 =

-1*(-1)^{5}*0 + 1*(-1)^{6}*(-6) + 1*(-1)^{7}*18 + 1*(-1)^{8}*(-42) =

0 + (-6) + (-18) + (-42) =

- 6 - 60 =

D = - 66

=

$\sf D_{a}=\left[\begin{array}{c|ccc}-2&3&1&-1\\\cline{1-4}4&-1&-1&1\\6&-2&5&1\\0&1&-2&1\end{array}\right]$

-2*c11 + 4*c21 + 6*c31 + 0*c41

(-1)*5*1 + (-1)*1*1 + 1*(-2)*(-2) - ( 1*5*1 + (-2)*1*(-1) + 1*(-2)*(-1) ) =

-5 + (-1) + 4 - 5 - 2 - 2 =

-2 - 9 =

= -11

$\sf D_{a}=\left[\begin{array}{c|ccc}-2&3&1&-1\\\cline{1-4}4&-1&-1&1\\\cline{1-4}6&-2&5&1\\0&1&-2&1\end{array}\right]$

3*5*1 + 1*1*1 + (-1)*(-2)*(-2) - ( 1*5*(-1) + (-2)*1*3 + 1*(-2)*1 ) =

15 + 1 + (-4) - (-5) - (-6) - (-2) =

12 + 13 =

= 25

$\sf D_{a}=\left[\begin{array}{c|ccc}-2&3&1&-1\\4&-1&-1&1\\\cline{1-4}6&-2&5&1\\\cline{1-4}0&1&-2&1\end{array}\right]$

3*(-1)*1 + 1*1*1 + (-1)*(-1)*(-2) - ( 1*(-1)*(-1) + (-2)*1*3 + 1*(-1)*1 ) =

-3 + 1 + (-2) - 1 - (-6) - (-1) =

-4 + 6 =

= 2

-2*c11 + 4*c21 + 6*c31 + 0*c41 =

-2*(-1)^{2}*(-11) + 4*(-1)^{3}*25 + 6*(-1)^{4}*2 =

22 + (-100) + 12 =

-78 + 12 =

Da = -66.

=

$\sf D_{b}=\left[\begin{array}{c|c|cc}3&-2&1&-1\\\cline{1-4}1&4&-1&1\\2&6&5&1\\-1&0&-2&1\end{array}\right]$

-2*c12 + 4*c22 + 6*c32 + 0*c42

1*5*1 + (-1)*1*(-1) + 1*2*(-2) - ( (-1)*5*1 + (-2)*1*1 + 1*2*(-1) ) =

5 + 1 + (-4) - (-5) -(-2) - (-2) =

2 + 9 =

= 11

$\sf D_{b}=\left[\begin{array}{c|c|cc}3&-2&1&-1\\\cline{1-4}1&4&-1&1\\\cline{1-4}2&6&5&1\\-1&0&-2&1\end{array}\right]$

3*5*1 + 1*1*(-1) + (-1)*2*(-2) - ( (-1)*5*(-1) + (-2)*1*3 + 1*2*1 ) =

15 + (-1) + 4 - 5 - (-6) - 2 =

18 - 1 =

= 17

$\sf D_{b}=\left[\begin{array}{c|c|cc}3&-2&1&-1\\1&4&-1&1\\\cline{1-4}2&6&5&1\\\cline{1-4}-1&0&-2&1\end{array}\right]$

3*(-1)*1 + 1*1*(-1) + (-1)*1*(-2) - ( (-1)*(-1)*(-1) + (-2)*1*3 + 1*1*1 ) =

- 3 + (-1) + 2 - (-1) - (-6) - 1 =

- 2 + 6 =

= 4

-2*c12 + 4*c22 + 6*c32 + 0*c42 =

-2*(-1)^{3}*11 + 4*(-1)^{4}*17 + 6*(-1)^{5}*4 =

22 + 68 + (-24) =

Db = 66.

=

$\sf D_{c}=\left[\begin{array}{cc|c|c}3&3&-2&-1\\\cline{1-4}1&-1&4&1\\2&-2&6&1\\-1&1&0&1\end{array}\right]$

-2*c13 + 4*c23 + 6*c33 + 0*c44

1*(-2)*1 + (-1)*1*(-1) + 1*2*1 - ( (-1)*(-2)*1 + 1*1*1 + 1*2*(-1) ) =

- 2 + 1 + 2 - 2 - 1  - (-2) =

1 - 1 =

= 0

$\sf D_{c}=\left[\begin{array}{cc|c|c}3&3&-2&-1\\\cline{1-4}1&-1&4&1\\\cline{1-4}2&-2&6&1\\-1&1&0&1\end{array}\right]$

3*(-2)*1 + 3*1*(-1) + 1*2*1 - ( (-1)*(-2)*1 + 1*1*3 + 1*2*3 ) =

- 6 + (-3) + 2 - 2 - 3 - 6 =

- 7 - 11 =

= - 18

$\sf D_{c}=\left[\begin{array}{cc|c|c}3&3&-2&-1\\1&-1&4&1\\\cline{1-4}2&-2&6&1\\\cline{1-4}-1&1&0&1\end{array}\right]$

3*(-1)*1 + 3*1*(-1) + (-1)*1*1 - ( (-1)*(-1)*(-1) + 1*1*3 + 1*1*3 ) =

- 3 + (-3) + (-1) - (-1) - 3 - 3 =

- 7 - 5 =

= -12

-2*c13 + 4*c23 + 6*c33 + 0*c44 =

-2*(-1)^{4}*0 + 4*(-1)^{5}*(-18) + 6*(-1)^{6}*(-12) =

0 + 72 + (-72) =

Dc = 0

=

$\sf D_{d}=\left[\begin{array}{ccc|c}3&3&1&-2\\\cline{1-4}1&-1&-1&4\\2&-2&5&6\\-1&1&-2&0\end{array}\right]$

-2*c14 + 4*c24 + 6*c34 + 0*c44

1*(-2)*(-2) + (-1)*5*(-1) + (-1)*2*1 - ( (-1)*(-2)*(-1) + 1*5*1 + (-2)*2*(-1) ) =

4 + 5 + (-2) - (-2) - 5 - 4 =

7 - 7 =

= 0

$\sf D_{d}=\left[\begin{array}{ccc|c}3&3&1&-2\\\cline{1-4}1&-1&-1&4\\\cline{1-4}2&-2&5&6\\-1&1&-2&0\end{array}\right]$

3*(-2)*(-2) + 3*5*(-1) + 1*2*1 - ( (-1)*(-2)*1 + 1*5*3 + (-2)*2*3 ) =

12 + (-15) + 2 - 2 - 15 - (-12) =

-1 - 5 =

= -6

$\sf D_{d}=\left[\begin{array}{ccc|c}3&3&1&-2\\1&-1&-1&4\\\cline{1-4}2&-2&5&6\\\cline{1-4}-1&1&-2&0\end{array}\right]$

3*(-1)*(-2) + 3*(-1)*(-1) + 1*1*1 - ( (-1)*(-1)*1 + 1*(-1)*3 + (-2)*1*3 ) =

6 + 3 + 1 - 1 - (-3) - (-6) =

10 + 8 =

= 18

-2*c14 + 4*c24 + 6*c34 + 0*c44 =

-2*(-1)^{5}*0 + 4*(-1)^{6}*(-6) + 6*(-1)^{7}*18 =

0 + (-24) + (-108)

Dd = -132

A = -66 / -66 = 1

B = 66/ -66 = -1

C = 0/-66 = 0

D = -132 / -66 = 2