(a) Prove that if S is a non-empty subset of a vector space V over a…

Question

(a) Prove that if S is a non-empty subset of a vector space V over a field F, then L(S), the linear span of S is the smallest subspace of V containing S.

(b) Determine whether or not the set $S = \{(1, 1, 2), (1, 2, 5), (5, 3, 4)\}$ forms a basis for the vector space $V = \mathbf{R}^3$ over the field R.

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