Math Is Fun Forum

deepz

Member

Registered: 2007-03-20

Posts: 10

Linear Algebra

Hi I need some help on a few proofs.

1) Prove that if {v1,....vn} is an orthonormal basis for R^n then {Qv1,....Qvn} is an orthonormal basis for R^n where Q is an orthogonal square matrix

2) S is a subspace of R^n with an orthogonal basis {v1,.....,vp} and {w1,......,wq} is an orthogonal basis for the orthogonal complement of S.

a-> Explain why {v1,...,vp,w1,......wq} is an orthogonal set that spans R^n
b-> Use part a to show that dim(S)+dim(orthogonal complement of S)=n

Thanks alot in advance!

freddogtgj

Member

Registered: 2006-12-02

Posts: 54

Re: Linear Algebra

No idea! What kind of question is this?!

Last edited by freddogtgj (2007-12-14 00:00:00)