# An Example of a 2-Dimensional Subspace of C[0,1]

1. Apr 16, 2014

### sheldonrocks97

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

Give an example of show that no such example exists.

A two dimensional subspace of C[0,1]

2. Relevant equations

None that I know of.

3. The attempt at a solution

I know that C[0,1] is a set of continuous functions but I'm not sure where to go after that.

2. Apr 16, 2014

### Dick

Define what 'two dimensional' means. That should be a clue.

3. Apr 16, 2014

### micromass

Staff Emeritus
Possibly a further clue: how would you find a two-dimensional subspace of $\mathbb{R}^n$?

4. Apr 16, 2014

### HallsofIvy

Staff Emeritus
Polynomials are continuous functions, aren't they? It should be easy to determine the dimension of a subspace of polynomial functions.