1. The problem statement, all variables and given/known data T: V --> W is a linear transformation where V and W are finite dimensional. If dim V is less than or equal to dim W, then T is one-to-one. True or false? 2. Relevant equations 3. The attempt at a solution First of all, I'm assuming that im(T) = W. Is that correct? If so, dim(im T) = dim(W). Dimension thm says dim(V) = dim(ker T) + dim(im T). So if dim(V) is less than or equal to dim(im T), then dim(ker T) = 0. Which means ker T is is as small as it can be, so T should be one-to-one. But this is wrong. The answer is supposed to be false. Can anyone help?