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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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