1. Math
  2. Algebra
  3. 2 12 points for each of the following either prove...

Question: 2 12 points for each of the following either prove...

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2. [12 points] For each of the following, either prove that it is a subspace or prove that it is not. For those that are subspaces, find a basis (you will need to prove that it is in fact a basis!) and state the dimension (a) The set of all matrices A M2x2(R) such that the sum of the entries in A is 0. (b) The set of all matrices A Mnxn (K) having det(A) = 0. (c) The set of all polynomials p(x) E P(C) such that all roots of p(x) are in R (d) The set of all polynomials p(x) e P(R) such that p(-x) = p(x).

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