Let the subset be defined by

1. Show that is a sub-space of

Because is a vector space and U inherits the same operations as . If is a sub-space then

a) U is non-empty, eg.

b) and , then

c)

2. Find a basis and dimension of

pretty simple, just the two column vectors above and so, dim(U) is 2.

3. How do I change the basis to a basis over ?