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March 5th, 2009, 09:51 AM   #1
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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.
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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.
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March 5th, 2009, 01:49 PM   #3
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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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