Find a basis for the subspace of $\mathbb{P}_2$ spanned by the given vectors. For any case, where the subspace is not all of $\mathbb{P}_2$, extend the linearly independent set you find to a basis of all $\mathbb{P}_2$.
- (a) $p_1 = -1 + x - 2x^2, p_2 = 3 + 3x + 6x^2, p_3 = 9$
- (b) $p_1 = 1 + x, p_2 = x, p_3 = −2 + 2x, p_4 = −3x$
- (c) $p_1 = 1 + x − 3x^2, p_2 = 2 + 2x − 6x^2, p_3 = 3 + 3x − 9x^2$
I think I've got very confused with the wording of it perhaps. If someone could just give me the general method and/or start me off with part (a), that would be amazing. Thank you so much in advance.