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Let V be an n-dimensional vector space and W a vector space that is isomorphic to...

Let V be an n-dimensional vector space and W a vector space that is isomorphic to V. Prove that W is also n-dimensional. Give a clear, detailed, step-by-step argument using the definitions of "dimension" and "isomorphic"

the Definiton of isomorphic:  Let V be an n-dimensional vector space and W a vector space that is isomorphic to V. Prove that W is also n-dimensional. Give a clear, detailed, step-by-step argument using the definitions of "dimension" and "isomorphic"

The Definition of dimenion: the dimension of V , written as dim V , is the number of vectors in a basis for V .

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