Linear Algebra with Applications (3rd Edition)

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
110.201 Linear Algebra 4th Quiz April 8, 2005 Problem 1 Let ~e i , i = 1 , 2 , 3 , 4 be the standard basis of R 4 . Is there an orthogonal matrix A with A~e 1 = 1 2 0 0 1 2 , A~e 2 = 1 2 0 0 - 1 2 , A~e 3 = 0 1 0 0 , A~e 4 = 0 0 2 0 or not? If so, find A , and if not, explain. Problem 2 Find an orthonormal basis for the subspace V R 3 spanned by the vectors 1 0 1 , 1 1 0 . Moreover, find a normal basis for the orthogonal complement of V . Problem 3 Let { 1 , ~α
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2 ,..., ~α k } be a set of mutually orthogonal vectors in R n . 1. Show that for any ~v ∈ R n , the vector ~v-(proj ~α 1 ( ~v ) + proj ~α 2 ( ~v ) + ··· + proj ~α k ( ~v )) is orthogonal to each of the ~α 1 , ~α 2 ,..., ~α k . 2. Verify this claim for R 3 with ~ α 1 = ~ e 1 , ~ α 2 = ~ e 2 , and letting ~v = 1 2 3 . Draw a picture. 1...
View Full Document

This homework help was uploaded on 01/23/2008 for the course MATH 201 taught by Professor Consani during the Spring '05 term at Johns Hopkins.

Ask a homework question - tutors are online