Finding a basis for vectors (a, b, c, d) in R⁴ where a ≠ 0

[fireb]

Homework Statement

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.

Homework Equations

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.
Thanks in advance.

 

[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.

 

[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?

 

[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.

 

[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.