Question

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

Answer 1

True

Answer 2

how would you justifiy it

Answer 3

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.

Answer 4

Use Rank Nullity Theorem

Answer 5

That would Definitely Hold True

Answer 6

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