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Suppose U and V are vector spaces. Define the function Z :

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Suppose U and V are vector spaces. Define the function Z :   UV by T (u) = 0V for every uU . Then by Exercise LT.M60, Z is a linear transformation. Formulate a condition on V that is equivalent to Z being an surjective linear transformation. In other words, fill in the blank to complete the following statement (and then give a proof): Z is surjective if and only if V is . (See Exercise ILT.M60, Exercise IVLT.M60.)

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