8. For all r E R", show that Use the above to show that for all A e Rnxn 1All Svn|All2 n|All, Alloo ValAll2 nAloo. 9. If A is nonsingular, show that the condition number K(A ] ) = maxmag( A) minmag(A) 10. Let A be a nonsingular matrix. Suppose Ar = b and A(x + 6x) = b + 6b. Show that SK(A) lox|I Give conditions on b, ob such that the equality holds for the above