Hello, I can't seem to figure out this problem about linear maps:

Assume v1,v2,..v5 is a basis of V and w1,w1,...w6 is a basis of W. Suppose you need to define a linear map T: V --> W. Which values would you assign to T(v1),T(v2),..T(v5) if it is required that dim(Null(T))=3, and that w1 is not in range(T).

I was wondering if the values of T(v1),..T(v5) should be scalars, or be variables with respect to w.

Thank you!!