# Basis and Dimension

• March 22nd 2007, 08:53 PM
tukeywilliams
Basis and Dimension
How would you find the dimension of the subspace of $\mathbb{P}_{3}$ spanned by the subset $\{t,t-1,t^{2}+1\}$?

How would you find a basis and dimension of the given subspace $\mathbb{R}^{3}\}$

$\{[a,a-b,2a+3b]|a,b, \in \mathbb{R}\}$ as a subspace of $\mathbb{R}^{3}$?
• March 22nd 2007, 10:03 PM
CaptainBlack
Quote:

Originally Posted by tukeywilliams
How would you find the dimension of the subspace of $\mathbb{P}_{3}$ spanned by the subset $\{t,t-1,t^{2}+1\}$?

The space spanned by {t, t-1, t^2+1} contains the polynomials 1, t, t^2,
which span a subspace of dimension 3.

RonL