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Unformatted text preview: B U Department of Mathematics Math 201 Matrix Theory Spring 2004 Second Midterm This archive is a property of Bogazi ci University Mathematics Department. The purpose of this archive is to organise and centralise the distribution of the exam questions and their solutions. This archive is a nonprofit service and it must remain so. Do not let anyone sell and do not buy this archive, or any portion of it. Reproduction or distribution of this archive, or any portion of it, without nonprofit purpose may result in severe civil and criminal penalties. 1. Let W be a subspace spanned by the following vectors { 1 1 1 , 1 / 3 1 / 3 2 / 3 } Find an orthonormal basis for W Solution: Let v 1 = 1 1 1 and v 2 = 1 / 3 1 / 3 2 / 3 .Then, v T 1 v 2 = (1 1 1) 1 / 3 1 / 3 2 / 3 = 1 / 3 + 1 / 3 2 / 3 = 0 Then, v 1 v 2 . So, u 1 = 1 k v 1 k = 1 / 3 1 1 1 = 1 / 3 1 / 3 1 / 3 and u 2 = 1 k v 2 k = 3 / 6 1 / 3 1 / 3 2 / 3 = 1 / 6 1 / 6 2 / 6 Therefore, { u 1 , u 2 } is an orthonormal basis for W . 2. Let A= 1 1 1 1 1 1 1 1 1 . Find the QR factorization of A....
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This note was uploaded on 04/29/2008 for the course MATH 201 taught by Professor Sadik during the Spring '08 term at Blue Mountain College.
 Spring '08
 sadik
 Math

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