January 29th, 2010, 12:41 PM  #1 
Senior Member Joined: Nov 2009 Posts: 129 Thanks: 0  linear transformation
Let V and W be finitedimensional vector spaces and T:V ? W be linear. Prove that if dim(V) < dim(W), then T cannot be onto. I have an idea that Assume dim(v) = m and dim(W) = n. Suppose W = {w1, w2, ... wn) and V = {v1, v2, ... vm). Vectors in W will maps onto all vectors in V however, one vectors in W will not get map onto V since m > n. Therefore T is not onto. Is this right? if so how do I reconstruct it? thanks. 
January 29th, 2010, 04:44 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,730 Thanks: 689  Re: linear transformation Quote:
 
January 29th, 2010, 11:51 PM  #3 
Senior Member Joined: Nov 2009 Posts: 129 Thanks: 0  Re: linear transformation
thanks


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