Problem 4. Let V be a vector space over F, and let (v₁, U2, U3, U4} be a linearly independent subset of V. Determine whether each of the following subsets of V is linearly independent or not. In each case, prove your claim. (a) A = {V₁ + V₁, V2 + V₁, V3+ V₁}. (b) B= {V₁-V₂, V₂ — V3, V3 — V₁, V₁}. (c) C = {V₁ V2, V2 — V3, V3 — V4, V4 — V₁}.

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