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November 10th, 2010, 07:02 AM   #1
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Isomorphism

This is a true/false question: All linear transformations from P3 to R2*2 are isomorphisms.
I think it is true because dim(P3)=dim(R2*2)=4, and ker(P3)=0. But the answer was false. I don't know why...So that means kernel is not 0?? But P3 has to be zero in order for R2*2 to be 0....
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November 10th, 2010, 08:31 AM   #2
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Re: Isomorphism

It is false. If are vector spaces with , then



is a linear transformation but it is not injective.

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