Proving Quadratic Basis for P(2): t2+2t+1, t2+t, t2+1

[mandygirl22]

Prove that t²+2t+1,t²+t, t²+1 is a basis for the space of quadratic polynomials P⁽²⁾.

 

[Mark44]

Prove that t²+2t+1,t²+t, t²+1 is a basis for the space of quadratic polynomials P⁽²⁾.

How do you show that the elements in a set are a basis for a vector space (which includes your function space)?