vector projection p of x onto y, and give the vector formula

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 21EQ
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The vectors x = (1, 1, 1)T and y = (1, 2, 2)T are in R3.


1) Find the vector projection p of x onto y, and give the vector formula for p  as the numerical vector of numbers.


2) Verify that p and xp are orthogonal.


3) Rewrite the formula to part (1) so that p = Px where P is a (projection) matrix? Show that P2 = P. (Hint: remember that xTyy = yyTx)

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