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December 8th, 2017, 07:16 AM   #1
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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.

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Last edited by skipjack; December 8th, 2017 at 10:08 AM.
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December 8th, 2017, 01:21 PM   #2
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What is "this"?
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December 8th, 2017, 04:54 PM   #3
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The word "this" refers to the title, I would assume.

I suggest reading this.
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December 9th, 2017, 01:09 PM   #4
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It is not clear (to me) what sort of equations are we looking at?
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December 9th, 2017, 01:52 PM   #5
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Quote:
Originally Posted by briankymely View Post
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.

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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?
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December 9th, 2017, 04:33 PM   #6
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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, 04:12 AM   #7
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Yeah thanks

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