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Determining whether a subset of a vector space forms a subspace

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Determining whether a subset of a vector space forms a subspace. i Determine whether each subset of a vector space forms a subspace. (a) The subset W of Pn that contains all polynomials of degree n or less that have all negative coefficients. (b) The subset W = R of R where addition is defined as a + y = cy and scalar multiplication is defined as c . a = a (c) The subset W of Rxn for which the trace - the sum of the diagonal entries of a matrix - is zero. (d) The subset W of Cla, b] such that lim f() = M where a < < < n and M # 0