Let vector u = <5,3,4,-1> , vector v = <3,-2,4,-1> and vector w = <4,1,2,-1>.

Determine whether or not the three vectors listed above are linearly independent or linearly dependent.

If they are linearly dependent, determine a non-trivial linear relation

0=a(vector u)+b(vector v)+c(vector w)

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Let define system of equations ,corresponding to a<5,3,4,-1>+b<3,-2,4,-1>+c<4,1,2,-1>=0

As,

`[[5,3,4],[3,-2,1],[4,4,2],[-1,-1,-1]]*[[a],[b],[c]]=[[0],[0],[0],[0]]` (i)

Let

`A=[[5,3,4],[3,-2,1],[4,4,2],[-1,-1,-1]]`

The homogenous system of equations (i) , has three variables and four eqtuations . So it has only Trivial Solution possible.

Therefore vector u,v and w are linearly independent.

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