Prove that every finite-dimensional vector space V of dimension n over a field F is isomorphic to

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Prove that every finite-dimensional vector space V of dimension n over a field F is isomorphic to the vector space Fⁿ of Exercise 19.

Data from Exercise 19

Generalize Example 30.2 to obtain the vector space Fⁿ of ordered n-tuples of elements of F over the field F, for any field F. What is a basis for Fⁿ?

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A First Course In Abstract Algebra

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Authors: John Fraleigh

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Prove that every finite-dimensional vector space V of dimension n over a field F is isomorphic to

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Let 1 2 n be a basis for V Let F n V be defined by a 1 a 2 a n a 1 1 a 2 2 a n n Because addition an...View the full answer

A First Course In Abstract Algebra

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