a) Prove that for an NxN-dimensional orthogonal matrix A, the determinant |A| = ±1. b) Consider the matrix = [a b] A = with a, b, c and d real-valued numbers. Under which condition(s) for a, b, c and d is the matrix A negative-definite?

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.1: The Determinants Of A Matrix
Problem 18E: Find the determinant of the matrix in Exercise 16 using the method of expansion by cofactors. Use a...
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a) Prove that for an NxN-dimensional orthogonal matrix A, the determinant |A|
b) Consider the matrix
A = [42]
b]
=
+1.
with a, b, c and d real-valued numbers. Under which condition(s) for a, b, c and d is the
matrix A negative-definite ?
Transcribed Image Text:a) Prove that for an NxN-dimensional orthogonal matrix A, the determinant |A| b) Consider the matrix A = [42] b] = +1. with a, b, c and d real-valued numbers. Under which condition(s) for a, b, c and d is the matrix A negative-definite ?
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