Question

Given a matrix mxn how would you determine if tha matrix is onto or one to one
T(x)=Ax

Answer 1

Do you just want the definitions?

Answer 2

thanks.

Answer 3

I think this works for me.

Answer 4

if its onto only, then that means for every element T(x), there is an element x which corresponds to it. And in onto, it doesn't matter if there are lots of distinct element x correpsonding to T(x). Such can be visualized like this:

now for one-to-one, for every element T(x), there must only be one element x corresponding to that. like this: