# Gram-Schmidt process Help

• Jul 9th 2011, 01:32 PM
kashmoneyrecord
Gram-Schmidt process Help
Hey guys,

I have a couple of questions that i need answered :( I have an exam coming up in a week and my prof. told me to answer a couple questions. I've worked out most of them but these three questions are really troubling me, if anyone can answer them and show me the steps I'd really appreciate it :(

1)Find an orthogonal basis for the subspace {[x,y,z] l 2x-y+z=0}

2) Use the Gram-Schmidt algorithm on the following set of vectors: {[1,1,-1,2],[0,1,-2,2],[2,2,-4,3]}

3)Given U=Span {[1,2,-3,-1],[3,-2,1,-4]} and x=[2,0,4,0] calculating the following:
a)ProjU(x)
b)ProjU(perpendicular sign) (x)
• Jul 9th 2011, 01:38 PM
girdav
Re: Gram-Schmidt process Help
What did you do? We won't answer the questions if you don't show your work.
• Jul 9th 2011, 01:44 PM
kashmoneyrecord
Re: Gram-Schmidt process Help
I sort of know how to do number 1 but the other two im completely puzzled, I can't show you my work if I don't know what to do :( If someone can answer it for me i can understand it from there. That's how i tend to learn, I can pick it up easier if the answer is shown to me and i can retrace and understand how a person gets to that answer.
• Jul 10th 2011, 07:37 AM
kashmoneyrecord
Re: Gram-Schmidt process Help
Can anyone help me out on this please :(
• Jul 10th 2011, 03:06 PM
Noxide
Re: Gram-Schmidt process Help
Quote:

Originally Posted by kashmoneyrecord
Hey guys,

I have a couple of questions that i need answered :( I have an exam coming up in a week and my prof. told me to answer a couple questions. I've worked out most of them but these three questions are really troubling me, if anyone can answer them and show me the steps I'd really appreciate it :(

1)Find an orthogonal basis for the subspace {[x,y,z] l 2x-y+z=0}

2) Use the Gram-Schmidt algorithm on the following set of vectors: {[1,1,-1,2],[0,1,-2,2],[2,2,-4,3]}

3)Given U=Span {[1,2,-3,-1],[3,-2,1,-4]} and x=[2,0,4,0] calculating the following:
a)ProjU(x)
b)ProjU(perpendicular sign) (x)

There's no real trick to any of these questions.
1. What is an orthogonal basis?
2. What is the purpose of the Gram-Schmidt process, what are each of its steps?
3. What is a projection?

Answer these questions, and only a few calculations will remain.