and another
basis 
.The basis vectors of S can be
expressed in terms of the Cartesian basis 
as
and 
and those of S' as
and 
.Given:
A basis and another
basis .The basis vectors of S can be
expressed in terms of the Cartesian basis as
and and those of S' as
and .
Asked: Find (a) the change of basis matrix P from S to S'; (b) the change of basis matrix Q from S' back to S.