Question: Let U, V, W be nitely generated vector spaces over F with dimension at least one. Prove or disprove: (U, W) '5 (V, W) if

Let U, V, W be nitely generated vector spaces over F with dimension at least one. Prove or disprove: (U, W) '5 (V, W) if and only if U E V. (hint: the question is not asking you to nd any isomorphisms.)

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