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Posted: **Tue Sep 07, 2021 7:35 am**

: 4 A Suppose That V Is A Finite Dimensional Vector Space Let T V V Be A Linear Map That Is Injective Prove That T 1 (40.68 KiB) Viewed 252 times

4. (a) Suppose that V is a finite-dimensional vector space. Let T :V → V be a linear map that is injective. Prove that T is an isomorphism. (b) Consider V = P2 (R) and W = {(x, y, z, k): k = x + 2z and x, y, z, k e R}. Are V and W isomorphic? Justify your answer.