1. You want V(k) to be linearly independent so that it will form a basis for R3. So that means if you interpret them as row vectors in a matrix and perform row reduction, the end result should be a matrix whose rank is 3. So what does the matrix being of full rank imply? And what values of k are suitable such that the matrix is of full rank?
2. Firstly determine the solution space of U(k). Then span(U(k1)) \subseteq span(V(k2)) if \forall v \ \text{where v is a vector in basis of U(k1)} \ , v \in span(V(k2)). ie. try to express every vector in the basis of U(k1) as a linear combination of V(k2). Take note of when this is possible (ie. which values of k1 and k2 permit that).
