October 2nd, 2018, 09:10 PM  #1 
Newbie Joined: Oct 2018 From: United States Posts: 2 Thanks: 0  Linear Combinations
Write the following statement in formal mathematical notation, including the sigma notation: a. Any linear combination of a finite number of linear combinations of a given set of vectors {x1,x2,...,xn}, generates a linear combination of the given set of vectors. b. Prove the statement in part a. 
October 2nd, 2018, 09:52 PM  #2 
Senior Member Joined: Aug 2012 Posts: 2,041 Thanks: 582  
October 2nd, 2018, 10:00 PM  #3 
Newbie Joined: Oct 2018 From: United States Posts: 2 Thanks: 0  No I am so sorry, I did not mean it to come off like that. I'm going to be honest, this is part of my homework that I have no idea how to do/start. I finished the rest of the homework but am now stuck on this problem and am now starting to get desperate.
Last edited by skipjack; October 3rd, 2018 at 01:22 AM. 
October 2nd, 2018, 10:39 PM  #4  
Senior Member Joined: Aug 2012 Posts: 2,041 Thanks: 582  Quote:
So working right to left, we have a finite set of vectors $x_i$. Then we have linear combinations of those: that is, expressions of the form ________. I'll let you fill that in; since you should be able to do that. And then we have a linear combination (the word finite is redundant since linear combinations are finite by definition) of those other linear combinations. And we are asked if that expression is in fact a linear combination of the original vectors. Does this help? The trick is to read the statement very carefully to understand what it means. Last edited by Maschke; October 2nd, 2018 at 10:45 PM.  
October 3rd, 2018, 01:37 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,703 Thanks: 1804  

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combinations, linear 
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