Determine whether or not the vectors u(1, 1, 2),ν (2,3, 1),
w(4,5,5) in R3 are linearly dependent.
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FORMULA TO BE IMPLEMENTED
LINEARLY DEPENDENT
A set of vectors { u, v, w } are said to be linearly dependent if there exists three scalers a, b, c , not all zero such that
CALCULATION
If possible there exists three scalers a, b, c such that
So
Equation (1) - Equation (2) gives
From Equation (1)
So
Hence from above
Thus there exists a non zero set of values of a, b, c such that
Hence the vectors u(1, 1, 2),v (2,3, 1),w(4,5,5) are linearly dependent.
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