Express and in terms of and
Hence each vector in is of the form
This shows that is a basis for which therefore has dimension 2. (Note that it also shows that is a subspace of
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
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 ?