Prove that every orthogonal matrix (QTQ = I) has determinant 1 or -1. (a) Use the product rule |AB| = |A||B| and the transpose rule |Q| = |QT|. (b) Use only the product rule. If | det Q|> 1 then det Q = (det Q)" blows up. How do you know this can't happen to Qn?
Prove that every orthogonal matrix (QTQ = I) has determinant 1 or -1. (a) Use the product rule |AB| = |A||B| and the transpose rule |Q| = |QT|. (b) Use only the product rule. If | det Q|> 1 then det Q = (det Q)" blows up. How do you know this can't happen to Qn?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 34E
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