Consider the follow sets of vectors. (i) Show that the set is linearly independent; (ii) use the Gram-Schmidt process to find a set of orthogonal vectors; (iii) determine a set of orthonormal vectors from the vectors in (ii).
a. v1 = (2,−1)t, v2 = (1, 3)t
b. v1 = (2,−1, 1)t, v2 = (1, 0, 1)t, v3 = (0, 2, 0)t
c. v1 = (1, 1, 1, 1)t, v2 = (0, 1, 1, 1)t, v3 = (0, 0, 1, 0)t
d. v1 = (2, 2, 0, 2, 1)t, v2 = (−1, 2, 0,−1, 1)t, v3 = (0, 1, 0, 1, 0)t, v4 = (−1, 0, 0, 1, 1)t