# Linear Alegbra and Vectors : Linear Dependence

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Determine whether or not the following set of vectors in R4 is linearly independent?

u=(1,0,3,0) v=(2,1,1,3) w=(1,2,-7,6)

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#### Solution Preview

Solution:

Set

k1u+k2v+k3w=0, we have k1(1,0,3,0)+k2(2,1,1,3)+k3(1,2,-7,6)=0

Thus.

k1+2k2+k3=0 ...

#### Solution Summary

A set of vectors are found to be not linearly dependent. Linearly independent vectors are analyzed.

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