# Linear Help

1. May 27, 2006

### gbacsf

I need some help in understanding what I need to do to solve these poblems, I can't get them started.

1. Find an orthogonal set of vectos that spans the same subspace as a,b,c.

a=(1,1,-1)
b=(-2,-3,1)
c=(-1,-2,0)

2. Use the Gram-Schmidt process to find and orthogonal basis that contains the vecto (-1,-4,2,-4)

2. May 27, 2006

### 0rthodontist

In 1., this IS the gram-schmidt process. Just apply it.

In 2., you have to pick some basis that contains that vector (try standard normal except for the vector) and then apply the gram-schmidt process.

3. May 27, 2006

### gbacsf

Thanks,

I finished off #1.

For the second question, what is meant by standard normal? Does that mean to use (0,1,0,0), (0,0,1,0) and (0,0,0,1) with the original vector in gram-schmidt to find the orthogonal basis?

4. May 28, 2006

### HallsofIvy

Staff Emeritus
Yes. Or (1, 0, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1) and the given vector, etc. In other words, any basis containing the given vector. By choosing 3 vectors from the "standard" basis you know they are independent, by making sure that your given vector has a non-zero number where the "missing" vector has a 1 you know that all 4 are independent and therefore, a basis.