For a 2 by 2 invertible matrix A, define the condition number tobe cond(A) = ||A|| ? ||A||-1. Assume that the matrixnorm is defined using the Euclidean vector norm.
(a) Find two 2by2 invertible matrices B and C such that cond(B +C) < cond(B) + cond(C).
(b) Find two 2by2 invertible matrices B and C such that cond(B +C) > cond(B) + cond(C).
(c) Suppose that A is a symmetric invertible 2by2 matrix. Findcond(2A) and cond(A2) in terms of cond(A).
(d)do the results from part (c) hold if A is not symmetric? Youcan either prove the results, or find counterexamples.
