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 November 10th, 2010, 07:02 AM #1 Member   Joined: Sep 2007 Posts: 49 Thanks: 0 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.... Thanks.
 November 10th, 2010, 08:31 AM #2 Newbie   Joined: Nov 2010 Posts: 3 Thanks: 0 Re: Isomorphism It is false. If $E,\;F$ are vector spaces with $E\neq \left\{{0}\right\}$ , then $0\;:\;E\rightarrow{F},\quad 0(x)=0\; \forall{x}\in{E}$ is a linear transformation but it is not injective. --- http://www.fernandorevilla.es/

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