Let V = {(x1, x2, x3, x4, x5) ∈ R5: x1−2x2 + 3x3−x4 + 2x5 = 0}. (a) Show that S = {(0, 1, 1, 1, 0)} is a linearly independent subset of V. (b)Extend S to a basis for V.

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