(a) Let V be a vector space and v₁, ..., V₂ € V. When do we say that vectors V₁, ..., Vn span V? (Give a precise definition.) (b) Consider vectors V1 = 1 2 V2 = 2 3 4 , V3 = 5 and v4= 8 (6) 10 in R³. (i) Do vectors V₁, V2, V3, V4 Span R³? (ii) Do vectors v₁ and v₂ span R³? (iii) Are vectors V₁, V2, V3, V4 linearly independent? Justify your answer in each case, and state precisely any theorems you use.

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