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February 11th, 2011, 06:12 AM  #1 
Member Joined: Feb 2011 Posts: 58 Thanks: 0  linear map T, finite dimensional vector space proof
if we let T: VV be a linear map, where V is a finite dimensional vector space, and suppose Rank()=Rank() prove that Im()=Im() 
February 11th, 2011, 09:19 AM  #2 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: linear map T, finite dimensional vector space proof We know that for we have so But the image of a linear operator is a vector space in its own right, and if vector spaces have the properties and it follows that 

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