Question

Faça o escalonamento

5x+12y+19z=8
2x+5y+8z=3
x+2y+3z=2

Answer 1

Olá


$\left\{\begin{array}{lll}5x+12y+19z=8\\2x+5y+8z=3\\x+2y+z=2\end{array}\right$


L2 = -5L2 + 2L1

$5x+12y+19z=8~~~~~ ~~~~~~ ~~~~~\cdot( 2)\\2x+5y+8z=3~~~~~~~~~~~~~~~ ~~\cdot(-5) \\ \\ \\ ~~~10x+24y+38z=16\\\underline{-10x-25y-40z=-15} \\ \\ ~-y-2z=1~~~~~~ ~~~ \longleftarrow\text{nova linha 2}$


L3 = -5L3 + L1

$5x+12y+19z=8\\x+2y+3z=2~~~~~~~~~~~~~~~~~~\cdot(-5) \\ \\ \\~~~ 5x+12y+19z=8\\\underline{-5x-10y-15z=-10}~\\\\2y+4z=-2~~~~~~\longleftarrow \text{linha 3 parcial}$


Vejamos como está as duas ultimas linhas

$-y-2z=1 \\ 2y+4z=-2$

Vamos tentar zerar o y

L3 = 2L2 + L3

$-y-2z=1 ~~~~~~ ~~~~ ~~\cdot(2)\\ 2y+4z=-2 \\ \\ \\ -2y-4z=2 \\ ~~~~\underline{2y+4z=-2} \\ ~~~~ ~0=0$


Sistema impossível.