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!