1.Given two invertible matrices A, B elements of Mn (R), show that?
cont .. 1.Given two invertible matrices A, B elements Mn (R), show that A ^ -1 – (A + B) ^ -1 = A ^ -1 (A + B ^ -1 ^ -1) ^ -1 A ^ -1 5. Definition. Let C in Mn (R). C is called symmetric if and only if A = Atranspose. Given symmetric matrices A, B elements Msubscript2 (R), show that AB is symmetric if and only if A, B commute with each other ei = AB BA. 6. If c is an eigenvalue associated to an element of Mn (R), show that c ^ k is associated an eigenvalue of A ^ k for some element k of N. 7. If an element of Mn (R) is a nilpotent matrix, show that the only eigenvalue of A is zero. 8. Let A and B elements of Mn (R) such that CX = Ax and Bx = bx. I. Show that (A + b) x = (c + b) x II. (AB) x = (cb) x
8. Let A and B elements of Mn (R) such that CX = Ax and Bx = bx. I. Show that (A + B) x = (c + b) x (A + B) x = Ax + Bx = Cx + BX = (b + c) x II. (AB) = x (Cb) x (AB) x = A (Bx) A = BX () = BAX = BCX = (cb) x
Pyxism Home Business Travel Opportunity (Pyxism)
