Let A and B be n x n matrices. 1. Show that A – AT is skew-symmetric. 2. Show that A+ AT is symmetric. 3. Let A and B be skew-symmetric matrices. Show that A + B is s symmetric.

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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B. Let A and B be n × n matrices.
1. Show that A – AT is skew-symmetric.
2. Show that A+ AT is symmetric.
3. Let A and B be skew-symmetric matrices. Show that A + B is s
symmetric.
4. Let A and B be symmetric matrices. Prove that the product A
symmetric if and only if AB = BA.
5. Show that if A is skew-symmetric, then the elements on the main diag
of A are all zero.
Transcribed Image Text:B. Let A and B be n × n matrices. 1. Show that A – AT is skew-symmetric. 2. Show that A+ AT is symmetric. 3. Let A and B be skew-symmetric matrices. Show that A + B is s symmetric. 4. Let A and B be symmetric matrices. Prove that the product A symmetric if and only if AB = BA. 5. Show that if A is skew-symmetric, then the elements on the main diag of A are all zero.
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