Question

20- Qual dos sistemas estão na forma escalonada?

X – Y + Z = 0 X – Y + Z = 0 2x –Y- 3z = 6 2y + z = 5 x-y+z=0

A) X – Z = 9 B) 2Y-3Z =5 C) 3y + 6Z = 5 D) x + y = 3 E) x+y=3

3Z=5 Y - Z = 2 2z = 4 x – z = 1 z=2​

Answer 1

x – y + z = 0  

x – y + z = 0  

2x –y- 3z = 6  

2y + z = 5  

x-y+z=0

tirando as iguais , ficamos com :

x – y + z = 0  

2x –y- 3z = 6  

2y + z = 5  

Escalonando:

1    -1    1   0

2    -1   -3   6

2     0    1   5

L2=L2-2L1

L3=L3-2L1

1     -1    1     0

0     1   -5    6

0     2   -1    5

L3=L3-2L2

1      -1       1      0 ==>x-y+z =0  =+> x-2,111-7/9=0 ==>x=2,88877

0      1      -5    6 ==>y-5z=6 ==>y-5*(-7/9)=6 ==>y=2,111..

0      0      9    -7 ==>9z=-7 ==> z=-7/9