Unformatted text preview: false. (20 points) (a) “Let x and y be ndimensional vectors. Then x · y = y · x .” (1 point) (b) “ AB = BA for any square matrices A and B .” (1 point) (c) Let X 2 denote XX . Then “( AB ) 2 = A 2 B 2 .” (1 point) (d) “If AB = B then A = I .” (1 point) 3. (a) Suppose that A and B are square matrices. Prove that ( AB ) k = A k B k if AB = BA . (1 point) (b) Show that ( AB ) k 6 = A k B k in general and conclude that ( A + B ) 2 does not equal A 2 + 2 AB + B 2 unless AB = BA . (1 point) 1...
View
Full Document
 Fall '07
 FACKLER
 Logic, Game Theory, Continuous function, Euclidean space

Click to edit the document details