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Examine the following vectors for linear dependence/independence
X1 = (a,b,c), X2 = (b,c,a), X3 = (c,a,b)
where a+b+c ≠ to zero.
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The given vectors are $X_1 = (a,b,c); \ X_2=(b,c,a); \ X_3 = (c,a,b)$ and the resultant matrix will be.
$\begin{bmatrix} a &b &c \\b &c &a \\c &a &b \end{bmatrix}$
The vector are linearly dependent if the determinant of this matrix is zero,
i.e.
$\begin{vmatrix} a &b &c \\b &c …
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