Applet : Coordinates with Respect to Change of Basis 
Let be any basis of . Let be its coordinates with respect to standard basis , where . Let v has coordinates with respect to basis .

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. 
So, By solving these two equations we can find the value of and . It's values are and 
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