1. Determine whether the following mapping is linear mapping.
2. Let be the
dimensional vector space. Let
be the basis of
.Define
by
. Then show that
is a linear mapping.
3. Let
be a linear mapping. Then the followings are equivalent.
4. Suppose that
is a linear mapping. Show that
are the subspace of
.
5. Let
be a linear transformation such that
. Find the matrix representation
of
relative to the usual basis
. Find also
relative to the basis
.