
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 20th, 2012, 07:12 AM  #1 
Newbie Joined: Apr 2012 Posts: 18 Thanks: 0  Dimensions, linear transformations
Prove that if A: X>Y is a linear transformation and V is a subspace of X then dimension of AV =< dimension of V. Deduce from here that rank (AB)=<rank B. AV means the subspace V transformed by the transformation V, i.e any vector in AV can be represented as Av, v belonging to V. I tried using the facts that AV is a subset of AX, V is a subset of X and i played around with the rank nullity theorem but could not prove it. Please help. 
September 21st, 2012, 08:22 AM  #2  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Dimensions, linear transformations Quote:
 

Tags 
dimensions, linear, transformations 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Linear Transformations in Linear algebra  matqkks  Linear Algebra  1  February 7th, 2012 01:39 PM 
Linear transformations  nuke  Linear Algebra  3  April 14th, 2011 12:32 PM 
Linear transformations  TsAmE  Linear Algebra  0  October 9th, 2010 06:54 AM 
Linear Transformations  wontonsoup  Linear Algebra  2  May 25th, 2009 04:35 PM 
Linear Algebra.Linear Transformations.Help!!  ypatia  Linear Algebra  1  March 2nd, 2009 06:28 PM 