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anonymous
 5 years ago
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
anonymous
 5 years ago
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

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0let 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.
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