Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: linear algebra with inverse of matrix.
Replies: 3   Last Post: Mar 18, 2013 12:47 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
W^3

Posts: 29
Registered: 4/19/11
Re: linear algebra with inverse of matrix.
Posted: Mar 16, 2013 1:45 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <010c295a-ec4c-43df-a2e5-bcf30115e590@googlegroups.com>,
mina_world@hanmail.net wrote:

> Hello teacher~
>
> nonzero 2 by 2 matrix A, B
>
> A^2 + B^2 = 0 and (A+B)^2 = 0
>
> (E : Identity matrix)
>
> (1) AB = -BA
>
> (2) (A^3)(B^3) = -(B^3)(A^3)
>
> (3) A+B+E has an inverse matrix.
>
> ---------------------------------------
> (1)
> (A+B)^2 = (A+B)(A+B)
> = A^2 + AB + BA + B^2 = 0
>
> Sinc A^2 + B^2 = 0, AB + BA = 0
> so, AB = -BA
>
> (2)
> Since AB = -BA,
> (A^3)(B^3) = AAABBB = AA(-BA)BB = AA(-B)(-BA)B
> =AA(-B)(-B)(-BA) = AA(-B^3.A)
> It means that ABBB = -BBBA
> so, AAABBB = -AABBBA = --ABBBAA = ---BBBAAA = -(B^3)(A^3)
>
> (3)
> Answer : inverse matrix ==> E-A-B
> How do you find it ?
>
> Of course, it's really true.
> (A+B+E)(E-A-B) = A-AA-AB+B-BA-BB+E-A-B = E


We know (1+z)^{-1} = 1 - z + z^2 - ... under certain circumstances.

So why not try (E+(A+B))^{-1} = E - (A+B) + (A+B)^2 - (A+B)^3 + ...

= E - (A+B) + 0 - 0 + ... = E - (A+B).



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.