October 2nd, 2018, 10:10 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, 10:52 PM  #2 
Senior Member Joined: Aug 2012 Posts: 2,156 Thanks: 630  
October 2nd, 2018, 11:00 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 02:22 AM. 
October 2nd, 2018, 11:39 PM  #4  
Senior Member Joined: Aug 2012 Posts: 2,156 Thanks: 630  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 11:45 PM.  
October 3rd, 2018, 02:37 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,269 Thanks: 1958  

Tags 
combinations, linear 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Vectors and linear combinations  Bencz  Algebra  1  June 20th, 2013 11:27 PM 
(Q) Linear combinations of solutions  ChidoriPOWAA  Real Analysis  2  October 10th, 2012 02:24 PM 
Complex Combinations Within Combinations Problem?  bugrocket  Advanced Statistics  2  January 23rd, 2011 05:02 PM 
Proof of a subset of integer numbers and linear combinations  uberbandgeek6  Number Theory  1  February 4th, 2010 07:27 AM 
linear combinations  kiwifruit  Linear Algebra  1  January 10th, 2010 02:16 PM 