Let 
be any basis of 
.
Let
be its coordinates
with respect to standard basis 
,
where 
.
Let v has coordinates 
with respect to basis
.
If 
, then
This gives unique value of 
,
.
In this Applet, default values of vector
,
and
are (-1,1) , (2,3) and
(-1,-1) are given respectively. You can enter values for
,
,
and click
OK to see the values of
and .
You can also change the values of
,
and
by selecting the scroll bar and using the sliders for X - axis and Y - axis at the bottom.
and
