4. (20%) Apply Gram-Schmidt Orthonormalization process to the vectors น1 = (1, 1,1),u2 = (1,0, -1),u3 = (2,1, -1) with respect to the stan- dard inner product.

Problem 6 :Let A and B be elements in (C). Suppose that AB - BA = c⋅(A - B) for some non-zero c ∈ C. Prove that there exists an invertible matrix P ∈ (C) such that AP and BP are upper-triangular matrices with the same diagonal entries.