S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Tue, 18 Jun 2013 06:13:03 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
TsAmE
 Post subject: Linear maps
PostPosted: Fri, 8 Oct 2010 21:20:47 UTC 
Offline
Senior Member

Joined: Mon, 19 Apr 2010 13:45:05 UTC
Posts: 61
Suppose that a function F: R^2 -> R^2 satisfies the conditions:

F(1, 0) = (3, 4), F(1, 1) = (7, 11), F(1, 2) = (11, 17)

Is F a linear map?

Im not sure how to do this. I know that you need to check if scalar multiplication and addition is preserved though, but I am not sure which equation to apply it to.
Top
 Profile  
 
outermeasure
 Post subject: Re: Linear maps
PostPosted: Sat, 9 Oct 2010 03:34:39 UTC 
Online
Moderator
User avatar

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6061
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
TsAmE wrote:
Suppose that a function F: R^2 -> R^2 satisfies the conditions:

F(1, 0) = (3, 4), F(1, 1) = (7, 11), F(1, 2) = (11, 17)

Is F a linear map?

Im not sure how to do this. I know that you need to check if scalar multiplication and addition is preserved though, but I am not sure which equation to apply it to.


Hint: (1,0)+(1,2)=2(1,1).

Hint 2: can you conclude F is a linear map just from knowing F at 3 points?

_________________
\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  
 
Shadow
 Post subject: Re: Linear maps
PostPosted: Sat, 9 Oct 2010 07:46:32 UTC 
Online
Moderator
User avatar

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12165
Location: Austin, TX
outermeasure wrote:
TsAmE wrote:
Suppose that a function F: R^2 -> R^2 satisfies the conditions:

F(1, 0) = (3, 4), F(1, 1) = (7, 11), F(1, 2) = (11, 17)

Is F a linear map?

Im not sure how to do this. I know that you need to check if scalar multiplication and addition is preserved though, but I am not sure which equation to apply it to.


Hint: (1,0)+(1,2)=2(1,1).

Hint 2: can you conclude F is a linear map just from knowing F at 3 points?


Ooh! I know! Pick me!

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination
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: therookie

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