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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I need help with this please, thanks.

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?

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