Math 220 Assignment

November 28, 2001

Due Friday, November 30

  1. Let S be the 2 \times 2 matrix

     
    (
    3/5 
    4/5
    4/5
    -3/5
    		)
    		  .  

    1. Find a line in R^{2} characterized by the property that the matrix S represents the reflection in that line relative to the standard basis of R^{2}.

    2. Find an orthogonal*1* matrix U for which

       U^{-1} S U 
      is a diagonal matrix.

  2. Is

     
    (
    -1 
    0
    1
    1
    		)
    		  
    the matrix of the reflection in some line?

Footnotes

  1. * An orthogonal matrix is a square matrix that is inverted by its transpose. See the assignment for Nov. 7 where the properties of such a matrix were explored.

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