Let V1,V2,.....Vk,V be vectors in a vector space V. and define W1 to be span(v1,V2,.....Vk) and W2 to be the Span(V1,V2.....Vk,V)

1) Find the necessary conditions on V such that dim(W1)=dim(W2)

2) State and prove a relationship involving dim(W1) and dim(W2), in the case where they dont equal each other.