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Suppose $$\{v_1,v_2,......v_n\}$$ is a set of linearly dependent vectors,none of them being a zero vector. Suppose $$c_1,c_2,...c_n$$ are the scalars ,not all zero, such that a linear combination of these are equal to zero vector. Then what will be the minimum number of non zero scalars ?

From Definition of Linear dependency what I have learned is if at least one scalar is nonzero then vectors are linearly dependent but the answer says the minimum number of non zero scalars are two. Please explain what am I missing it?

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  • $\begingroup$ What is the situation if exactly one scalar is nonzero? $\endgroup$ – saulspatz May 10 '18 at 17:00
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Note that

$$c_1v_1+c_2v_2+...+c_nv_n=0$$

then assume wlog $$c_1=c_2=...=c_{n-1}=0 \implies c_nv_n=0\implies c_n=0$$

therefore there exist at least two non zero scalar coefficients.

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