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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).](https://homework-api-assets-production.s3.ap-southeast-2.amazonaws.com/uploads/store/124599331/160556896750ca858a5ae45e29b6ad237dd078f05b.png)