Question: Let V and V' be vector spaces over the same field F, and let V be finite dimensional over F. Let dim(V) be the dimension

Let V and V' be vector spaces over the same field F, and let V be finite dimensional over F. Let dim(V) be the dimension of the vector space V over F. Let ∅ : V → V' be a linear transformation.

a. Show that ∅[VJ is a subspace of V'.

b. Show that dim(∅[V]) = dim(V) - dim(Ker(∅)).

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a By group theory we know that V is a subgroup of V Let V and a F Then a a shows that V is closed under multiplication by scalars in F Thus V is a sub... View full answer

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