how do you find the spanning set for U ∩ V where U={(x,y.0): x and y are complex} and V= sp { (1,2,3,), (i,-i, 10)}?
Clearly: U contains only vectors from V that have z-coordinate 0, thus if you take any linear combination from V, you have to require that , hence .
This means that is 1-dimensional and that any single vector that you get by chosing and will therefore span that intersection.
Take for example, , hence . This gives the vector
of .