Math CentralQuandaries & Queries


Question from tousif, a student:

Find the 2 x 2 matrix which represents a reflection in the line y = x?
Please help....

Hi Tousif,

Suppose the matrix is matrix and pointis a point in the plane. Under a reflection in the line y = x the point point is transformed to transformed point. 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?


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