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1. Let v1,…,vn be a basis of a vector space V. Show that (a) for any...

1. Let v1,…,vn be a basis of a vector space V. Show that

(a) for any non-zero λ1,…,λn∈R, λ1v1,…,λnvn is also a basis of V.

(b) Let ui=v1+⋯+vi, 1≤i≤n. Show that u1,…,un is a basis of V.

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