Question: If T: V U is a linear transformation where dim V - n, show that TST = T for some isomorphism S: V

If T: V → U is a linear transformation where dim V - n, show that TST = T for some isomorphism S: V → V. [Let {e1,..., er, er+1,...,en] be as in Theorem 5 §7.2. Extend {T(e1),..., T(er)} to a basis of V, and use Theorem 1 and Theorems 2 and 3, §7.1.]

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