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December 8th, 2017, 07:16 AM  #1 
Newbie Joined: Dec 2017 From: Ottawa Posts: 2 Thanks: 1  Linear dependency and independence
Can this be explained by use of one solution, no solution or infinitely many solutions? If not, just summarize it for me the way you understand it. Sent from my SMG955W using Tapatalk Last edited by skipjack; December 8th, 2017 at 10:08 AM. 
December 8th, 2017, 01:21 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,528 Thanks: 589 
What is "this"?

December 9th, 2017, 01:09 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,528 Thanks: 589 
It is not clear (to me) what sort of equations are we looking at?

December 9th, 2017, 01:52 PM  #5  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,197 Thanks: 872  Quote:
First if a set of linear equations is "independent", that is, each vectors whose components are the coefficients of the same unknown are independent (equivalently the matrix of coefficients has nonzero determinant), then there must be exactly one solution and vice versa. If the system of equations is NOT independent, then there may be no solution or an infinite number of solutions. Conversely, if a system of linear equations has either no solution or an infinite number of solutions then the equation are "dependent". Is that what you mean?  
December 9th, 2017, 04:33 PM  #6  
Newbie Joined: Dec 2017 From: Ottawa Posts: 2 Thanks: 1  Quote:
Sent from my SMG955W using Tapatalk  
December 14th, 2017, 04:12 AM  #7 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,197 Thanks: 872  

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dependency, independence, linear 
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