# Linear dependency and independence

#### 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.

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Forum Staff
What is "this"?

#### skipjack

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

#### mathman

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

#### Country Boy

Math Team
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?

#### briankymely

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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#### Country Boy

Math Team
Yeah thanks

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While driving at 70 mph, probably!