Write the solution set of the given homogeneous system in
parametric vector form
x1+2x2+12x3=0
2x1+x2+12x3=0
-x1+x2 =0
Thank you in advance!
Answer
x1+2x2+12x3=0..............(1)
2x1+x2+12x3=0............(2)
-x1+x2 =0.........(3)
from (3) x2 = x1.........(4)
putting (4) in (1) or in (2) we get , x2 =
-4x3
thus, the parametric solution is :-
x1 = x2 = -4x3
x1+2x2+12x3=0 eqn1
2x1+x2+12x3=0 eqn2
-x1+x2 =0 eqn3
eqn3*2+eqn2=x2+4x3
eqn1+eqn3=x2+4x3
and
x1=x2
hence
x1=x2=-4x3