5. For matrices AE RPX4, the spectral norm is defined as, a'A' Ax ||A||2 = sup 240 r's Further, the eigenvalues of A'A are the squares of the singular values of A, so sometimes the definition of the spectral norm is expressed as ||A||2 = max(A), where max denotes the largest singular value of A. (a) Verify that the spectral norm is a norm. Recall that a norm must satisfy the following axioms for any A, B, C & RPX and any a R. = i. ||a4||-|a|||A|| ii. ||A + B|| ||A||| + ||B||| iii. A 20 with equality if and only if A=0. (b) Show that the spectral norm is sub-multiplicative for square matrices. That is, for A, BE RPP, ||AB||2A2B2