Let v₁ = (1,3,5), v² = (-2, 1, 7) and let P be the plane spanned by v¹ and v². (That is, P = (v1, v2).) Let √3 = (7,7,1). Show that (v1, v2, v³) as follows: First show that is in P. • Next explain why (v1, v2, v3) is a subspace of P. • Next explain why P = (v1, v2) is a subspace of (v1, v2, v3). • Conclude that (v1, v2, v3) is the exact same set as P.

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