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August 24th, 2015, 09:42 AM   #1
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Linear Independence and Linear Dependence.

If $\left \{ u,v \right \}$, $\left \{ v,w \right \}$ and $\left \{ w,u \right \}$ LI are subsets of a vector space V, then $\left \{ u,v,w \right \}$ is LI?
Note: LI is Linear Independence.
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August 24th, 2015, 11:19 AM   #2
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What happens if $\vec u$, $\vec v$ and $\vec w$ are co-planar? Can they be distinct and co-planar?

Last edited by skipjack; August 24th, 2015 at 12:24 PM.
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August 24th, 2015, 12:18 PM   #3
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(1, 0) and (0, 1) are linearly independent.
(1, 0) and (1, 1) are linearly independent.
(0, 1) and (1, 1) are linearly independent.
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August 24th, 2015, 02:44 PM   #4
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No, if it is co-planar they would LD (linear dependent). and q I do now ????
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August 24th, 2015, 03:05 PM   #5
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So you have that, if the three vectors are co-planar, they would be LD.
Can you find three co-planar vectors that, pairwise are LI? Hint: see Country Boy's post.

Last edited by v8archie; August 24th, 2015 at 03:08 PM.
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August 24th, 2015, 03:10 PM   #6
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The general case of Country Boy's example would be $\vec w = a\vec u + b \vec v$ where $a$ and $b$ are non-zero real numbers. The main advantage of writing it like this is that we get any number of dimensions for free with the notation.
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