Comments on: (Linear Algebra) How to determine the expression of this linear mapping ? http://www.mathstudenthelp.info/algebra/linear-algebra-how-to-determine-the-expression-of-this-linear-mapping Let us help you add it up! Mon, 21 May 2012 10:21:24 +0000 http://wordpress.org/?v=2.7 hourly 1 By: cheeser1 http://www.mathstudenthelp.info/algebra/linear-algebra-how-to-determine-the-expression-of-this-linear-mapping/comment-page-1#comment-6989 cheeser1 Tue, 22 Dec 2009 16:52:59 +0000 http://www.mathstudenthelp.info/algebra/linear-algebra-how-to-determine-the-expression-of-this-linear-mapping#comment-6989 If you can find a basis for R2 and figure out what this does to the basis, you are done. There are two approaches:       • Use the standard basis -- calculations are harder, but the matrix is easy to find       • Use a "nice" basis -- calculations are easy, but the matrix is harder to find. I will do the first method. Where does (1,0) go when reflected by that line? It goes to (-3/5,4/5). And where does (0,1) go? It goes to (4/5,3/5). So the matrix is simply: [ -3/5 4/5 ] [ 4/5 3/5 ] which are those two things, put into the columns.<br><b>References : </b><br> If you can find a basis for R2 and figure out what this does to the basis, you are done.

There are two approaches:

      • Use the standard basis — calculations are harder, but the matrix is easy to find
      • Use a "nice" basis — calculations are easy, but the matrix is harder to find.

I will do the first method. Where does (1,0) go when reflected by that line? It goes to (-3/5,4/5).

And where does (0,1) go? It goes to (4/5,3/5).

So the matrix is simply:

[ -3/5 4/5 ]
[ 4/5 3/5 ]

which are those two things, put into the columns.
References :

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