1. (a) In R3, represent all the linear combinations of v=(2,0,1) and w=(0,1,2), give a geometric interpretation. And find a vector which is not a combination of v and w.

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.