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I am a bit confused... Linear combination means

$$F(X)=af(x_1)+bf(x_2) + \cdots$$

and linearly independent means

$$af(x_1)+bf(x_2) + \cdots=0$$

where $a=b=\cdots=0$

My question: is a linear combination linearly independent or linearly dependent as $F(x)$ is not $0$?

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    Both meanings you give look quite wrong. Can you try stating things again more carefully, and *completely*?2012-12-29
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    A linear comb. is always lin. independend. If you are working in a vector space we have $\alpha v = 0 \iff \alpha = 0$ if $v \neq 0$. But per definition is $0$ lin. independend.2012-12-29
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    You are indeed a bit confused about what linearly independent means. A *set* of vectors $\{x_1,\ldots,x_n\}$ is linearly independent if $a_1x_1+\cdots+a_nx_n=0$ implies that $a_i=0$ for all $i$. Which makes your question nonsense.2012-12-29
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    ok, well, the only thing i could understand is linear combinations is always linearly independent, I am sorry as I am student of applied Maths and in 1999 I studied linear algebra for the last time... Thank you all for the patience...2012-12-29

4 Answers 4