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I was confused about how to do this so any explanations would be appreciated!
Let u = [u_1, u_2, u_3], v = [v_1, v_2, v_3], and w = [w_1, w_2, w_3] be three vectors in R^3. Show that S = {u, v, w} is linearly independent if and only if the determinant of
u_1 u_2 u_3
v_1 v_2 v_3
w_1 w_2 w_3
is not equal to 0.
(consider the transpose and the Independence Test Method)
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