The counterpositive is "If T is onto, then m<=n" It's easier to do it by the theorem that says that the dimensions of the kernel and of the image of T add to n.Prove: A linear Map T:Rn->Rm is not onto if m>n.
The only way I have thought about doing this problem is by proving the contrapositive:
If m<=n then T:Rn->Rm is onto.
I would start by letting there be a transformation
matrix with dimension mxn.
Then the only thing I can think of doing is using the rank nullity thm to show that the dimension of the range=dimension of v. Does anyone know of any other ways to go about this or if my way would be correct? Thank you so much