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

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

$\displaystyle \{[a,a-b,2a+3b]|a,b, \in \mathbb{R}\}$ as a subspace of $\displaystyle \mathbb{R}^{3}$?