Suppose {\(v_1, ..., v_m\)} spans a vector space V and suppose \(v_i\) is linear combination of the preceding vectors. Show that {\(v_1, ..., v_{i-1}, v_{i+1}, ..., v_m\)}spans V. How to start?

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are {v1 ,..,vn} independent ?

Hmm... suppose i) they are independent ii) they are dependent It is not specified in the question. So, I would like to know how it works for these two cases.

In English, (sort of), if a set of vectors (let's call it S) which contains v[i] spans V, then if you take away v[i], the resulting set would still span V, yes? :)

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