testing header
Math Goodies is a free math help portal for students, teachers, and parents.
Free Math
Interactive Math Goodies Software

Buy Math Goodies Software
testing left nav
Math Forums @ Math Goodies
Math Forums @ Math Goodies
Home | Profile | Active Topics | Members | Search | FAQ
Save Password
Forgot your Password?

 All Forums
 Homework Help Forums
 Matrix Identity
 New Topic  Reply to Topic
 Printer Friendly
Author Previous Topic Topic Next Topic  

Average Member

9 Posts

Posted - 03/27/2012 :  09:57:11  Show Profile  Reply with Quote
For each of the following statements, select whether the statement is true or false for all n n matrices A, B , C. (Note that you are being asked whether the statement is true or false for all n n matrices A, B, C, not just for some A, B, C.)

1. (2 A - 8 B)(2 A + 8 B) = 4 A^2 - 64 B^2

2. A(2 I - 8 BA) = (2 I - 8 AB)A

3. A ≠ 0 and AB = A ⇒ B = I

4. (-2 I + AA^T)^ T = -2 I + AA^T

I think the answer is 1-true, 2-false, 3-true, 4-false.
Is it correct or wrong.
Go to Top of Page


3059 Posts

Posted - 03/27/2012 :  10:09:00  Show Profile  Reply with Quote
1. This appears to require commutativity.
2. Check associativity.
3. What if A doesn't have an inverse?
4. Be careful with transpositions.
Go to Top of Page
  Previous Topic Topic Next Topic  
 New Topic  Reply to Topic
 Printer Friendly
Jump To:
Math Forums @ Math Goodies © 2000-2004 Snitz Communications Go To Top Of Page
This page was generated in 0.03 seconds. Snitz Forums 2000
testing footer
About Us | Contact Us | Advertise with Us | Facebook | Blog | Recommend This Page

Copyright © 1998-2014 Mrs. Glosser's Math Goodies. All Rights Reserved.

A Hotchalk/Glam Partner Site - Last Modified 16 Dec 2014