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ashleyi376 ashleyi376
wrote...
11 years ago
Could someone please show me the solution to this problem in Linear algebra? Thanks a lot!

Determine the expression of the linear mapping in the plane, which reflects all points with respect to the straight line y=2x.
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wrote...
#1
11 years ago
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.
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