Problems

Let be the linear transformation

a) Find the matrix of wrt. the standard basis

2 let
extend the basis to
Show that the space of all real valued continuous functions on is infinite dimensional

Consider the set they are linearly independent and belong to the above space hence the space should be infinite
4. Consider the subspace of and in

a) find bases for and

basis of we can extend this to basis of and

a) Find the basis of
b)Find a complement of containing
c) Modify and get a complement of span not containing and find a projection into the span along