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## Homework Statement

If u1 and u2, u2 and u3, u1 and u3 are Linearly Independent, does it follow that {u1,u2,u3} is Linearly Independent?

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- Thread starter symsane
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- #1

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If u1 and u2, u2 and u3, u1 and u3 are Linearly Independent, does it follow that {u1,u2,u3} is Linearly Independent?

- #2

Defennder

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[tex]a_1 u_1 + a_2 u_2 + a_3 u_3 = \textbf{0}[/tex].

Suppose one of the a

- #3

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## Homework Statement

If u1 and u2, u2 and u3, u1 and u3 are Linearly Independent, does it follow that {u1,u2,u3} is Linearly Independent?

No. Try to find a counterexample (this is possible in R^2).

- #4

lurflurf

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if u1 and u2 are linearly dependent does it follow that

v1 and v2 are linearly independent where

v1=a*u1+b*u2

v2=c*u1+d*u2

or

if span(V)=n

does that mean any n vectors are linearly independent?

- #5

Defennder

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Oops, can't believe I missed such a simple counter-example.No. Try to find a counterexample (this is possible in R^2).

- #6

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No. Try to find a counterexample (this is possible in R^2).

I could not find a counter example. I think it is LI.

- #7

Mark44

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- #8

Defennder

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You can try thinking about the orthogonal standard basis vectors.I could not find a counter example. I think it is LI.

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