1. The problem statement, all variables and given/known data Say I have a matrix: [3 -2 1] [1 -4 1] [1 1 0] Is this matrix onto? One to one? 2. Relevant equations 3. The attempt at a solution I know it's not one to one. In ker(T) there are non trivial solutions to the system. But since I've confirmed there is something in the ker(T), does this indicate that it is also not onto as well? I know that being an onto transformation is the Im(T) where it represents all transformed vectors. The reduced matrix I got was this: [ 1 0 1/5 | c-b/5] [0 1 -1/5 | b/5] [0 0 0 | a - b ] Can 0 = a-b ever? If I put in random values for a,b,c the system will be inconsistent usually.