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（a）Suppose A ∈ M3(R) is nonzero, but A · A = 0. What are the possibilities...

（a）Suppose A ∈ M3(R) is nonzero, but A · A = 0. What are the possibilities for the dimension of the kernel of A?
（b）Let V be a finite dimensional vector space, and U ⊂ V a subspace.Show that there exists a linear map T:V→V with Im(T) = U.
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