Question

If S a subspace of R^3 consisting of all vectors orthogonal to g =[1, 2, 4], how I show S is a subspace of R^3; Find the basis of S

Answer 1

let a, b a vector in S, ie orthogonal vectors to g.
a transpose * g = 0 , b transpose * g = 0
then (a+b)transpose * g = 0.
similarly ka transpose * g = 0.
Therefore S is a subspace.

from orthogonality
p+2q+4r = 0.
and (-2,1,0) (-4,0,1) are special solutions(from the lecture) and they are the basis.