Thread: 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)

What did you do? We won't answer the questions if you don't show your work.

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.

Can anyone help me out on this please

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.