A plane P containing the origin can be specified by giving a unit vector u that is orthogonal to

A plane P containing the origin can be specified by giving a unit vector u that is orthogonal to the plane. That is, let P = {x ∈ R3 : u · x = 0}. A reflection across P is the linear transformation that maps each point x to its “mirror image” directly across P, as illustrated in Figure II.16. Prove that, for a plane containing the origin, this reflection is represented by the 3 × 3 matrix I − 2uuT.Write out this matrix in component form too.

 
 
 

 
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