# Orthogonalizing a basis by gram schmidt process

1. Nov 6, 2012

### Kamekui

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

(a.) Find an orthonormal basis of R^4 spanned by {1,1,1,1},{1,0,0,1}, and {0,1,0,1}.
(b.) Use the inner product to express {2,2,2,2} as a linear combination of the basis vectors. Do not solve the equations.

2. Relevant equations

gram schmidt orthogonalization and then normalizing

3. The attempt at a solution

(a.) I used gram schmidt orthogonalization and then normalized to get:

1/2{1,1,1,1}, 1/2{1,-1,-1,1}, 1/2{-1,1,-1,1}

(b.) I'm not sure how to do this, any help would be appreciated.

2. Nov 6, 2012

### LCKurtz

So you want$$(2,2,2,2) = \frac {c_1}2 (1,1,1,1)+\frac {c_2}2 (1,-1,-1,1)+\frac {c_3}2 (-1,1,-1,1)$$What happens if you take the inner product of both sides of that with one of your basis vectors?