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 December 8th, 2017, 08:16 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 SM-G955W using Tapatalk Thanks from mathman Last edited by skipjack; December 8th, 2017 at 11:08 AM.
 December 8th, 2017, 02:21 PM #2 Global Moderator   Joined: May 2007 Posts: 6,641 Thanks: 625 What is "this"?
 December 8th, 2017, 05:54 PM #3 Global Moderator   Joined: Dec 2006 Posts: 19,974 Thanks: 1850 The word "this" refers to the title, I would assume. I suggest reading this.
 December 9th, 2017, 02:09 PM #4 Global Moderator   Joined: May 2007 Posts: 6,641 Thanks: 625 It is not clear (to me) what sort of equations are we looking at?
December 9th, 2017, 02:52 PM   #5
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Quote:
 Originally Posted by briankymely 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 SM-G955W using Tapatalk
Gosh, I hate "Tapatalk"!

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 non-zero 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, 05:33 PM   #6
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Quote:
 Originally Posted by Country Boy Gosh, I hate "Tapatalk"! 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 non-zero 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?
Yeah thanks

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December 14th, 2017, 05:12 AM   #7
Math Team

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Quote:
 Originally Posted by briankymely Yeah thanks Sent from my SM-G955W using Tapatalk
While driving at 70 mph, probably!

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