# HW9_14 - M 3 40L C S H omew ork Set 9 3 2 1 5 3 u 2 2 u 3 1...

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M 340L CS Homework Set 9 1. Let           1 2 3 3 2 1 5 3 , 2 , 1 , 3 . 0 1 4 1 u u u b a. Form the matrix 1 2 3 U u u u and confirm that the columns of U are orthogonal by computing . T U U b. Express b as a linear combination of 1 2 , u u and 3 . u (That is, solve . Ux b Be clever about using T U to do this.) 2. Let 1 2 2/ 3 1/ 3 1/ 3 , 2/ 3 2/ 3 0 u u a. Form the matrix 1 2 U u u and confirm that the columns of U are orthogonal by computing . T U U b. Normalize the columns and confirm that . T U U I 3. Answer true or false to the following. If false offer a simple counterexample. a. Every orthogonal set in n is linearly independent.

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