Linear dependency and independence

Dec 2017
2
1
Ottawa
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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skipjack

Forum Staff
Dec 2006
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The word "this" refers to the title, I would assume.

I suggest reading this.
 

mathman

Forum Staff
May 2007
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It is not clear (to me) what sort of equations are we looking at?
 

Country Boy

Math Team
Jan 2015
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Alabama
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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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?
 
Dec 2017
2
1
Ottawa
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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