I need the answer as soon as possible 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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Answered: 2. Let A E Mn (R) be a skew-symmetric…

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 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.