Prove or disprove the following statements. (a) Let V and W be finite dimensional vector spaces...
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Prove or disprove the following statements. (a) Let V and W be finite dimensional vector spaces over a field K such that dim V dim W. Then any linear map T: V W has a nonzero kernel. (b) Any subset of a linearly independent set is linearly independent. (c) Any subset of a linearly dependent set is linearly dependent. Prove or disprove the following statements. (a) Let V and W be finite dimensional vector spaces over a field K such that dim V dim W. Then any linear map T: V W has a nonzero kernel. (b) Any subset of a linearly independent set is linearly independent. (c) Any subset of a linearly dependent set is linearly dependent.
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