Introduced the concept of a linear transformation of the plane. Showed
that reflection in a line through the origin is a linear transormation.<br>
      <br>
For more background on linear transformations see Section 9.5 of Lawson's book, and also take a look at the Open
Corseware notes from MIT <a
 href="http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/positive-definite-matrices-and-applications/linear-transformations-and-their-matrices/MIT18_06SCF11_Ses3.6sum.pdf">here</a>.