Sup1X>se that A and 8 arc m x m matrices that commute:

Chapter , Problem 24

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Sup1X>se that A and 8 arc m x m matrices that commute: that is. AB = BA. Prove that the binomial formula holds for A and 8 when k = 2 and k = 3. Specifically. prove that and Elementary Linear Algebra: A Matrix Approach, 2nd Edition, page: 121 No part of any book may be reproduced or transmitted by any means without the publishers prior permission. Use (other than qualified fair use) in violation of the law or Terms of Service is prohibited. Violators will be prosecuted to the full extent of the law. User: Thomas McVaney Page 4 of 10 (b) Usc mathematical induction to extend the results in pan (a) to any positive integer k. (c) For the matricc' A and 8 on page 117. >how 8 3 = 0 and that A :md 8 commute. Then use (b) to prove k(k I) , A4 = 1, + tB + -- 2 - s- fork :: 2.