assign5

assign5 - MATH 235/W08: Orthogonality & Gram-Schmidt,...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 235/W08: Orthogonality & Gram-Schmidt, Assignment 5 Hand in questions 3,9,11,13,14 by 9:30 am on Wednesday March 5, 2008. Contents 1 Orthogonal Pairs 2 2 Representation using Orthogonal Complement 2 3 Basis and Distance *** 2 4 Orthogonal Basis 2 5 Orthogonal Basis for Columns Space 2 6 Orthogonal Matrix 2 7 Orthogonal Matrix Two 3 8 True-False Questions 3 9 Angles Between Vectors *** 3 10 Orthonormal Bases 3 11 Basis and Nearest Vectors *** 4 12 Gram-Schmidt Procedure 4 13 Gram-Schmidt Procedure and Inner Products *** 4 14 MATLAB: Predator-Prey System *** 5 1 1 Orthogonal Pairs Determine which pairs of vectors are orthogonal; find the norms of each vector. a) u = i √ 2 1 , v = i √ 2- 1 b) u = 1 / 2 1 / 2 1 / 2 1 / 2 , v = 1 / √ 2- √ 2 2 Representation using Orthogonal Complement Let u 1 = (3 , , 1) T , u 2 = (0 , 1 , 0) T , and y = (0 , 3 , 10) T . Let W = span { u 1 , u 2 } . Represent y as the sum of a vector in W and a vector in the orthogonal complement of W . 3 Basis and Distance *** Let V be the nullspace of A where A = 1- 1- 3 2 1 2- 1 4 2 1 3 4 3 2 1 5 6 and let v = ( 2 9- 3 32- 83 ) T ....
View Full Document

This note was uploaded on 04/27/2010 for the course MATH 235 taught by Professor Celmin during the Winter '08 term at Waterloo.

Page1 / 5

assign5 - MATH 235/W08: Orthogonality & Gram-Schmidt,...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online