# Finding basis probelm

1. Dec 11, 2009

### fireb

1. The problem statement, all variables and given/known data
Let S be the form of (a, b,c ,d )in R4, given a not equal to 0. Find the basis that is subset of S.

2. Relevant equations

3. The attempt at a solution
I got a(1,0,0,0), b(0,1,0,0), c(0,0,1,0), d(0,0,0,1) as basis. a not = 0
But i wasn't sure what the significances of a not = to 0 means

Any help would be appreciated.

2. Dec 11, 2009

### LCKurtz

It means find four elements of R4 that are linearly independent and all of whose first components are non-zero. That would comprise such a basis.

3. Dec 12, 2009

### HallsofIvy

However, the set of all (a, b, c, d) in R4 such that $a\ne 0$ is NOT a subspace and so does NOT have a basis. Are you sure you have read the problem correctly?

4. Dec 12, 2009

### LCKurtz

I'm thinking the OP may have the problem stated correctly since he/she calls S a set. They just seek a basis for R4 choosing only from that set.

5. Dec 13, 2009

### HallsofIvy

Ah! You are right. I misread it. The problem is NOT to find a basis for S but to find a basis for R4 such that the first component of each basis vector is not 0.
I would be inclined to take the "standard" basis and change the first component of each to a simple non-zero number. Then check to see if they are still independent.