Problem 6. Let Pd (2, C) denote the vector space ofC-polynomials in two variables, of degree ? d.
Define a linear map S : P2(2, C) ? P2(C) by S(p) := p(z, z)(where z is a variable for the polynomials in P2(C)).
(a) Prove that S is surjective and that Skew2(2, C) ?ker(S).
(b) Give an example of a polynomial in ker(S) Skew2(2, C).Hence write down a basis for ker(S).
