So I have been having some difficulties with this problem:

Let distinct real numbers. The Lagrange polynomials are defined by

a) Compute the Lagrange Polynomials associated with n=2 and . Evaluate .

b) Prove that is a basis for .

The first part of a i think i more or less have, here is what I did:

Then I add those together and I get 7. Is this correct atleast?

As for evaluate , how am i supposed to go about doing this?

For part B I would need to show that the set is both linearly independent and spans . Any suggestions on how to go about doing this?

Thanks for any help you can provide!