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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=wThe matrix A will have more columns than rows (more unknowns than equations), so there will be infinitely solutions (more than one mapping from avin V to awin W).

I'm stumped by part a). I'm not seeing how m>n guarantees that there arew's in W that aren't part of R(T).

A nudge in the right direction would be greatly appreciated.

Thanks.

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# Homework Help: Linear Transformation - Onto

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