solns5 - MATH 235/W08 Orthogonality Gram-Schmidt SOLUTIONS...

This preview shows page 1 - 4 out of 11 pages.

MATH 235/W08: Orthogonality & Gram-Schmidt,SOLUTIONS to Assignment 5Solutions to questions 3,9,11,13,14.Contents1 Orthogonal Pairs21.1Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22 Representation using Orthogonal Complement22.1Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 Basis and Distance ***33.1Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33.1.1A Helpful MATLAB Program with Output. . . . . . . . . . . . . . . . . . .44 Orthogonal Basis55 Orthogonal Basis for Columns Space56 Orthogonal Matrix67 Orthogonal Matrix Two68 True-False Questions69 Angles Between Vectors ***69.1Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .710 Orthonormal Bases711 Basis and Nearest Vectors ***711.1 Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .712 Gram-Schmidt Procedure813 Gram-Schmidt Procedure and Inner Products ***813.1 Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .914 MATLAB: Predator-Prey System ***1014.1 Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101
1Orthogonal PairsDetermine which pairs of vectors are orthogonal; find the norms of each vector.a)u=i21,v=i21b)u=1/21/21/21/2,v=1/20201.1SolutionBEGIN SOLUTION:
2
6
(a) Find a basis forV.(b) Find the distance fromvtoV.3.1SolutionBEGIN SOLUTION:
1010401202
. After a permutation ofcolumns 3 and 4, this matrix is in the formparenleftbiggIE

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture