Use this definition of an orthogonal matrix: We say that Q ∈ Mn×n(R) is an orthogonal matrix if QtrQ = In, where In is the n × n identity matrix (b) Suppose that A is an n × n orthogonal matrix. Show that det A = ±1.

Use this definition of an orthogonal matrix: We say that Q ∈ Mn×n(R) is an orthogonal matrix if QtrQ = In, where In is the n × n identity matrix (b) Suppose that A is an n × n orthogonal matrix. Show that det A = ±1.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CR: Review Exercises

Problem 66CR

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Use this definition of an orthogonal matrix: We say that Q ∈ M_n_×_n(R) is an orthogonal matrix if Q^trQ = I_n, where I_n is the n × n identity matrix

(b) Suppose that A is an n × n orthogonal matrix. Show that det A = ±1.

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