Question

Faça o escalonamento do sistema..

-x+2y+2z=0
2x+5y-z=3
x+y-z=1

Answer 1

Olá


$\left\{\begin{array}{lll}-x+2y+2z~=0~\\2x+5y-z~=3~\\x+y-z~=~1\end{array}\right$

L2 = 2L1 + L2

$-x+2y+2z=0~~~~~~ ~~~\cdot( 2) \\ 2x+5y-z=3 \\\\-2x+4y+4z=0 \\ \underline{~~~~2x+5y-z=3} \\\\ 9y+3z=3~~~~~ ~~ \longleftarrow~~~~~\text{nova linha 2}$

L3 = L3 + L1


$-x+2y+2z=0 \\ \underline{~~~x+y-z=1} \\ \\ 3y+z=1~~~~~ ~~\longleftarrow \text{linha 3 parcial}$


L3 = -3L3 + L2

$9y+3z=3\\ 3y+z=1 ~~~ ~~~~ ~~~~~~\cdot (-3) \\ \\ ~~~~ 9y+3z=3\\ \underline{-9y-3z=-3 } \\ \boxed{0 =0}$


Sistema impossível.