title: Affine transformation
body: <p>I am trying to solve the below problem. I don't have much knowledge in <a href="http://en.wikipedia.org/wiki/Affine_transformation" rel="nofollow noreferrer">Affine transformations</a>. Could someone help me answer this question:</p>
  
  <p>Find a 3x3 matrix representing a 2D affine transformation of homogeneous coordinates (i.e. every point <code>[x,y]</code> is represented as a column vector <code>[x, y, 1]</code>), which transforms a square <code>[0,0],[1,0],[1,1],[0,1]</code> into a parallelogram <code>[0,1],[1,1],[2,2],[1,2]</code>.</p>