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March 5th, 2009, 09:51 AM  #1 
Newbie Joined: Mar 2009 Posts: 3 Thanks: 0  Linear Algebra.Linear Transformation.Help
Suppose T is the linear transformation on R^3 that takes each point (x,y,z) to (x+y+z, x+y,z). Describe what T^1 does to the point (x,y,z). Thanks in advance. 
March 5th, 2009, 01:48 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,582 Thanks: 610  Re: Linear Algebra.Linear Transformation.Help Quote:
x'=x+y+z y'=x+y z'=z Since x+y=u will give the same values for x' and y' for any x and y with that u, you can't invert T.  
March 5th, 2009, 01:49 PM  #3 
Senior Member Joined: Feb 2009 Posts: 172 Thanks: 5  Re: Linear Algebra.Linear Transformation.Help
Observe for example that and . Hence but . So T is not injective wich means it doesn't have an inverse.


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