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#1 2007-04-04 15:49:55

quackensack
Member
Registered: 2007-02-27
Posts: 47

Proof help

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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