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linearly independent equation [help]

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elec350

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hello
pls define the linearly independent equation and linearly dependent equation for me.
 

the system is independent if the only sulotion to:

a1V1 + a2V2+...+AnVn = 0

a1,a2,An - constants
V1,V2,...,Vn - vecrtors representing the euations

is: a1=0,a2=0,..,An=0


example
2x1+3x2+0x3=0 => V1=(2,3,0)
4x1+6x2+0x3=0 => V2=(4,6,0)
4x1+5x2+1x3=0 => V3=(4,5,1)

here 2V1 -1V2+0V3=0 this means the system is dependent

1x1+3x2+7x3=0
 

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    elec350

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hi mayyan
your definition has ambiguity. pls expln more.
 

Hi elec350,
mayyan is right and I wanna add that linearly independent equation can be represented by matrix of a1, a2, a3...
 

hope the attachment will help
 

an equation which contain solutions independent and not equal to zero
like
a1b1+a2b2+.....=0
in this equation
a1b1 is independent from a2b2 ( this can be proved from wronskian theorem )
wronskian
w= det(a1b1,a2b2/d(a1b1)d(a2b2))
also
a1b1, a2b2 not equal to zero
 

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