# Linear Dependence of Vectors

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Question :

Prove that ( 1 , 3 , 2 ) , ( 1 , - 7 , - 8 ) , ( 2 , 1 , - 1 ) of V3( R) is linearly independent.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

a1 , a2 , a3 be scalars belonging to R.

The associated matrix is formed by the coefficients of a1 , a2 and a3

Rank of A = 2 < no. of variables ( a1 , a2 , a3 )

Therefore, the given vectors are linearly independent.

For detailed step by step solution, please see the attached solution file.

Â© BrainMass Inc. brainmass.com December 24, 2021, 6:30 pm ad1c9bdddf>https://brainmass.com/math/linear-algebra/linear-dependence-vectors-118972