S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Thu, 20 Jun 2013 10:23:08 UTC

View unanswered posts | View active topics


Board index » High School and College Mathematics » Matrix Algebra

All times are UTC [ DST ]



Post new topic Reply to topic  Page 1 of 1
  [ 3 posts ] 
  Print view Previous topic | Next topic 
Author Message
sadabo
 Post subject: Find the matrix inversion
PostPosted: Wed, 1 Sep 2010 00:02:29 UTC 
Offline
S.O.S. Newbie

Joined: Tue, 24 Aug 2010 19:51:27 UTC
Posts: 2
Find the inverse, if possible

[2 3]
[3 5]
Top
 Profile  
 
dmoran
 Post subject:
PostPosted: Wed, 1 Sep 2010 03:29:15 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame

Joined: Thu, 1 Jan 2004 06:47:21 UTC
Posts: 2735
Location: Norman, Oklahoma
Here's what you do.

Add the identity matrix onto the existing matrix so you get

[2 3 1 0]
[3 5 0 1]

Then, do row operations until you get the identity matrix on the left side. The last two columns will be the inverse.

Dave

_________________
Please do not send me private messages asking for help unless you're asking about a post that I've made. Private Messages about threads that I've not participated in will be deleted and not answered.
Top
 Profile  
 
outermeasure
 Post subject: Re: Find the matrix inversion
PostPosted: Wed, 1 Sep 2010 16:06:42 UTC 
Offline
Moderator
User avatar

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6071
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
sadabo wrote:
Find the inverse, if possible

[2 3]
[3 5]


Just use
\begin{pmatrix} a&b\\c&d \end{pmatrix} \begin{pmatrix} d&-b\\-c&a \end{pmatrix} =(ad-bc)\begin{pmatrix} 1&0\\0&1 \end{pmatrix}

_________________
\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  Page 1 of 1
  [ 3 posts ] 

Board index » High School and College Mathematics » Matrix Algebra

All times are UTC [ DST ]

Who is online

Users browsing this forum: No registered users

You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
Contact Us | S.O.S. Mathematics Homepage
Privacy Statement | Search the "old" CyberBoard

users online during the last hour
Powered by phpBB © 2001, 2005-2011 phpBB Group.
Copyright © 1999-2013 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA