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

[sheldonrocks97]

Homework Statement

Give an example of show that no such example exists.

A two dimensional subspace of C[0,1]

Homework Equations

None that I know of.

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.

 

[Dick]

Homework Statement

Give an example of show that no such example exists.

A two dimensional subspace of C[0,1]

Homework Equations

None that I know of.

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.

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

 

[micromass]

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

 

[HallsofIvy]

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