Please help me with these questions step by step, show all details of calculations and provide clear reference, thank you so much!

(a) Verify that the following three vectors v1 = (1,-1, 1); v2 = (-2, 3, -1) and v3 = (1, 2, -4) form a basis for R3

(b) Starting from the basis (v1 , v2 ,v3) and using the Gram-Schmidt process , construct the orthonormal basis for R3

(c) Repeat the Gram-Schmidt process for the set of vectors v₁^'= (1, -1, 1); v₂^'= (-2, 3, -1); and v₃^'= (1, 0, 2)

(d) Compare results of (b) and (c) and explain the difference.