Question

resolva os sistemas lineares usando escalonamento:

Answer 1

• Escalonamento

-3(i) + (ii)

-3x + 3x -6y -4y +3z +5z = -3*0 + 10

-10y +8z = 10 ← (II)

(III) -(I)

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

y -2z = -1 ← (III)

(II) +10(III)

(-10 + 10)y +(-2 -20)z = 10 -10

-22z = 0

z = 0

→ Substituindo no sistema

$\begin{cases} x +2y -z = 0\\0x -10y +8z = 10\\0x +0y +z = 0 \\\end{cases}$

Se z = 0

-10y +0 = 10

y = -10/10 = -1

Se y = -1

x -2 + 0 = 0

x = 2

S = {2 , -1 , 0}