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Prove the following: Let V and W be vector spaces of equal (finite) dimension, and let T:...

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Advance Math

Prove the following:

Let V and W be vector spaces of equal (finite) dimension, andlet T: V ? W be linear. Then the following are equivalent.

(a) T is one-to-one.

(b) T is onto.

(c) Rank(T) = dim(V).

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