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2. Let A E Mn (R) be a skew-symmetric matrix, i.e. AT A. Prove that (a) x" Ax = 0 for all r E R". (b) The eigenvalues of A are pure imaginary, i.e. X= ib with be R. (c) The determinant of A is positive or zero.

2. Let A E Mn (R) be a skew-symmetric matrix, i.e. AT A. Prove that (a) x" Ax = 0 for all r E R". (b) The eigenvalues of A are pure imaginary, i.e. X= ib with be R. (c) The determinant of A is positive or zero.

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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2. Let A e M, (R) be a skew-symmetric matrix, i.e. AT = -A. Prove that (a) x' Ax = 0 for all x E R". (b) The eigenvalues of A are pure imaginary, i.e. A= ib with beR. (c) The determinant of A is positive or zero.
Transcribed Image Text:2. Let A e M, (R) be a skew-symmetric matrix, i.e. AT = -A. Prove that (a) x' Ax = 0 for all x E R". (b) The eigenvalues of A are pure imaginary, i.e. A= ib with beR. (c) The determinant of A is positive or zero.
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