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Math · Algebra
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1. In each of the following cases, either prove that the given subset W is a subspace of V, or show why it is not a subspace of V (a) Coo (R), W is the set of functions f E V for which lim f(z) 0. 00 (b) V Coo (R), W is the set of functions f E V for which f (4) 1 (c) V M2x2 (R), W is the set of matrices whose square is the zero matrix (i.e., those matrices A with A2 the zero matrix (d) V R W is the subset of vectors T1, T2, T3, for which 3 r2 zi, for all n 1 and in general T4 n+2 n +1

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