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Mathematics 7 Online
OpenStudy (anonymous):

Justify true or false If the Nulity(T)=0, then the linear transformation T: V -> U is one-to one

OpenStudy (anonymous):

True

OpenStudy (anonymous):

how would you justifiy it

OpenStudy (anonymous):

would this hold ? True Rank Nullity theorem states Dim(Ker(T)+Dim(Range)=Dim(Domain) Since Nullity(T)=0 It follows that Dim(Range)=Dim(Domain) Thus one to one.

OpenStudy (anonymous):

Use Rank Nullity Theorem

OpenStudy (anonymous):

That would Definitely Hold True

OpenStudy (zarkon):

suppose Tx=Ty then Tx-Ty=0 T(x-y)=0 since nullity(T)=0 x-y=0 thus x=y hence T is one-to-one

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