Homework Help: Orthogonal Projection of vector Y onto subspace S

1. Oct 23, 2012

ElijahRockers

1. The problem statement, all variables and given/known data

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.

3. The attempt at a solution

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

I dont have a book so any reference links would be helpful. I have watched numerous videos and read through paul's online notes but i cant seem to find anything about this problem. Exam tomorrow. :(

2. Oct 23, 2012

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(ATA)-1ATY

is that correct?

3. Oct 23, 2012

jdolan8

Math 311? Im working on this one too

4. Oct 23, 2012

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.