Let V and W be finite dimensional vector spaces over F and T : V W is a linear map. Prove that T is an isomorphism if and only if {T(v 1 ),T(v 2 ),...,T(v n )} is a basis for W whenever {v 1 ,v 2 ,...,v n } is a basis for V .

6. Let V and W be finite dimensional vector spaces over F and T :V + W is a linear map. Prove that T is an isomorphism if and only if {T(v1), T(v2), ...,T(Un)} is a basis for W whenever {V1, V2, ..., Un} is a basis for V. 6. Let V and W be finite dimensional vector spaces over F and T :V + W is a linear map. Prove that T is an isomorphism if and only if {T(v1), T(v2), ...,T(Un)} is a basis for W whenever {V1, V2, ..., Un} is a basis for V