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Problem 6. Let Pd (2, C) denote the vector space of C-polynomials in two variables, of...

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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).

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a In one of the previous part we have seen that a basis ofis Alsowe know that a basis of is and abasis of is Now by definition    See Answer
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