15. Let W be the solution space to the system Ax = 0. Determine whether the set {u, v} spans W. [1 1 1 1] A = 1 0 1 0 0
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15. Let W be the solution space to the system Ax = 0. Determine whether the set {u, v} spans W. [1 1 1 1] A = 1 0 1 0 0 1 01 a. u = (1, 0, −1, 0), v = (0, 1, 0, -1) b. u = (1, 0, -1, 0), v = (1, 1, -1, -1)
19. Let p₁ = 1 + x², P₂ = 1 + x + x², and q₁ = 2x, q₂ = 1 + x². Use Theorem 4.3.2 to show that span{p₁, P₂} = span{q₁, 92}.
23. Prove that if {u, v} spans the vector space V, then {u, u + v} spans V.