Reference: Linear Algebra, 5th ed., Friedberg, Insel, and Spence Pearson (problem not from textbook)

Let V = {(x₁, x₂, x₃, x₄, x₅): x₁ 2x₂ + 3x₃ x₄ + 2x₅ = 0}. Note that v = (1, 2, 1, 0, 0) is a vector in V . Use column correspondence to find a basis for V that includes v.