- #1

- 74

- 0

## Homework Statement

Can you find a basis {p

_{1}, p

_{2}, p

_{3}, p

_{4}} for the vector space ℝ[x]

_{<4}s.t. there does NOT exist any polynomials p

_{i}of degree 2? Justify fully.

## Homework Equations

## The Attempt at a Solution

We know a basis must be linearly independant and must span ℝ[x]

_{<4}. So intuitively if there are no polynomials of degree 2 we cannot span V. It just isn't possible.

I'm just struggling to justify it rigorously.

Many thanks - I appreciate the time and help.