Given (x₁ = 1/2(1,1,1,-1)T) and (x₂ = 1/6(1,1,3,5)T), verify that these vectors form an orthonormal set in ℝ⁴. Extend this set to an orthonormal basis for ℝ⁴ by finding an orthonormal basis for the null space of ([1 1 1 1 1 3 -1 5]T).