Linear Transformation -- Onto I'm having trouble with the first part of the following problem: Let T be a linear transformation from an n-dimensional space V into an m-dimensional space W. a) If m>n, show that T cannot be a mapping from V onto W. b) if m<n, show that T cannot be one-to-one. Part b) I can see. I think. T(v) = Av = w The matrix A will have more columns than rows (more unknowns than equations), so there will be infinitely solutions (more than one mapping from a v in V to a w in W). I'm stumped by part a). I'm not seeing how m>n guarantees that there are w 's in W that aren't part of R(T). A nudge in the right direction would be greatly appreciated. Thanks.