Question: 3. Matrix multiplication. (a) Consider the following matrices. 1 0 -2 2 O 6 10 A = B = 4 3 C = -3 -1

3. Matrix multiplication. (a) Consider the following matrices. 1 0 -2 2 O 6 10 A = B = 4 3 C = -3 -1 , D = 1 -1 4 8 5 2 O 1 4 Perform the indicated operations, if defined; or explain why it is undefined. i. AB, ii. BA, iii. BC, iv. CD, v. DC, vi. DA. (b) Suppose that A and B are nonsquare matrices. Under what conditions are both AB and BA defined? Could the nonsquare matrices be defined so that AB = BA? (c) Suppose that A a 0 where a and b are real numbers. Show by induction that O b an 0 An = 0 bn for positive integer n

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