Orthogonal Projection of vector Y onto subspace S

[ElijahRockers]

Homework Statement

Let S be the linear span of the orthogonal set:

{[3 2 2 2 2]^T,[2 3 -2 -2 -2]^T,[2 -2 3 -2 -2]^T}

Calculate the orthogonal projection of Y = [1 2 -1 3 1]^T onto S.

The Attempt at a Solution

Not sure how to go about this...

Do i find a vector that is orthogonal to S, and then project Y onto it?

I don't have a book so any reference links would be helpful. I have watched numerous videos and read through paul's online notes but i can't seem to find anything about this problem. Exam tomorrow. :(

 

[ElijahRockers]

I think I found it. If A is the matrix of the vectors spanning S, then the orthogonal projection of Y onto S is...

A(A^TA)^-1A^TY

is that correct?

 

[jdolan8]

Math 311? I am working on this one too

 

[ElijahRockers]

Yep. Our teacher doesn't use visual or geometric examples at all, some it's all pretty abstract to me... I have been hitting the khan academy though so hopefully I'll be alright.