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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
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Re: Linear Algebra.Linear Transformation.Help

Quote:
 Originally Posted by ypatia 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.
If you write T explicity, you have the following:
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 $T(1,0,0)=(1+0+0, 1+0,0)=(1,1,0)$ and $T(0,1,0)=(0+1+0, 0+1,0)=(1,1,0)$. Hence $T(1,0,0)=T(0,1,0)$ but $(1,0,0)\neq (0,1,0)$. So T is not injective wich means it doesn't have an inverse.

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