Let V be the vector space of the polynomials of degree $\displaystyle \leq $ 2 over $\displaystyle \mathbb{R}$.

Prove that the polynomials:

$\displaystyle p_1 = 2T^2 + T + 1 $

$\displaystyle p_2 = 4T^2 + T$

$\displaystyle p_3 = -2T^2 + 2T + 1$

span, or are a generating system of, V.

If I solve the system of linear equations- how do I prove that they span V?

Thanks.