Question: 1. Suppose V is an infinite-dimensional vector space. a) Prove that for any positive integer n, V contains a set of n linearly independent vectors.

1. Suppose V is an infinite-dimensional vector space. a) Prove that for any positive integer n, V contains a set of n linearly independent vectors. [3] b) Prove that if V' is a subspace of V and if V/V is finite-dimensional, then V is infinite-dimensional. [3] c) Prove that if T: V - W is a linear map, where W is finite- dimensional, then T has an infinite-dimensional nullspace. [4]

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