Explain why the dot product of x and y equals the dot product of Px and Py. Then (Px) T  (Py) = xTy tells us that pT P = I for any permutation. With x = (1, 2, 3) and y = (1, 4, 2) choose P to show that Px · y is not always x · Py.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 30E
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Explain why the dot product of x and y equals the dot product of Px and Py. Then (Px) T  (Py) = xTy tells us that pT P = I for any permutation. With x = (1, 2, 3) and y = (1, 4, 2) choose P to show that Px · y is not always x · Py.

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