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| Math Central | Quandaries & Queries |
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Question from tousif, a student: Find the 2 x 2 matrix which represents a reflection in the line y = x? |
Hi Tousif,
Suppose the matrix is 
and 
is a point in the plane. Under a reflection in the line y = x the point is transformed to 
. Thus
Expand this matrix equation to yield two linear equations. These equations are valid for all choices of p and q. What happens when p = 0 and q = 1? What does this tell you abut the transformation matrix?
Penny
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