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Problem 2. Fix 0 < 0

Problem 2. Fix 0 < 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer 2.2 not 2.1 

For 2.2 ignore the part that mentions Problem 1 - it is irrelevant 

Problem 2. Fix 0 < 0 <T, and define A E M2(R) by cos 0 – sin 0 COS sin 0 COS O 2.1. Show that A is orthogonal (as in Problem 1), by verifying directly that AAT = I = A"A. V1 2.2. Now let v = ER² be nonzero. Find the angle y between v and Av. Use U2 this, together with the fact that || Av|| = ||v|| (see Problem 1) to describe in one sentence the geometric relationship between v and Av.
Transcribed Image Text:Problem 2. Fix 0 < 0 <T, and define A E M2(R) by cos 0 – sin 0 COS sin 0 COS O 2.1. Show that A is orthogonal (as in Problem 1), by verifying directly that AAT = I = A"A. V1 2.2. Now let v = ER² be nonzero. Find the angle y between v and Av. Use U2 this, together with the fact that || Av|| = ||v|| (see Problem 1) to describe in one sentence the geometric relationship between v and Av.
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