N n a i a 2 a n n a b 2 a 2 2 ab b 2 a b 2 a 2 ab ba

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n × n . ( A + I )( A 2 + A n × n . ( A + B ) 2 = A 2 + 2 AB + ( A + B ) 2 = A 2 + AB + BA + B 2 . This is only equal to A 2 + 2 AB + B 2 when AB = BA , which in general is not true. ( A + B ) 2 = A 2 + AB AB + B 2 = A 2 + B 2 . This is only equal to A 2 + 2 AB + B 2 when or B = 0 nn , which in general is not true. ( A + B ) 2 = A 2 BA + BA + B 2 = A 2 + B 2 . This is only equal to A 2 + 2 AB + B 2 when or B = 0 nn , which in general is not true. ) B 2 A = 0 nn A = 0 nn
AB BA A = 0 0 0 0 0 0 0 1 0 B =
9. 1/1 points | Previous Answers HoltLinAlg1 3.2.034. Find an example that meets the given specifications. 3 × 3 nonzero matrices A and B such that 1 1 1 0 0 0 1 0 1 10. 1/1 points | Previous Answers HoltLinAlg1 3.2.037. Find an example that meets the given specifications. 2 × 2 matrices A , B , and C that are nonzero, where 1 1 1 1 AB = 0 33 A = 0 1 0 0 0 0 0 0 0 B = A B AC = BC A = , B 1 6 6 1 6 1 1 6 C = but . =
11. 1/1 points | Previous Answers HoltLinAlg1 3.2.040. Determine if the statement is true or false, and justify your answer. You may assume that A and B are matrices. If A and B are diagonal matrices, then so is
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