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Unformatted text preview: Math 2940 Solutions, Fall 2011 Section 2 . 4 1 ) Since A is 3 × 5 and B is 5 × 3, AB and BA are, respectively, 3 × 3 and 5 × 5. Since D is 3 × 1, ABD = ( AB ) D is 3 × 1. Since D is 3 × 1 and B is 5 × 3, DB is not defined, so DBA is not defined. Finally, B and C have different dimensions so B + C is not defined and neither is A ( B + C ). 6 ) First the correct rule: ( A + B ) 2 = ( A + B )( A + B ) = AA + AB + BA + BB = A 2 + AB + BA + B 2 . When A = 1 2 0 0 and B = 1 0 3 0 we have ( A + B ) 2 = 1 2 0 0 2 + 1 2 0 0 1 0 3 0 + 1 0 3 0 1 2 0 0 + 1 0 3 0 2 = 1 2 0 0 + 7 0 0 0 + 1 2 3 6 + 1 0 3 0 = 10 4 6 6 , but A 2 + 2 AB + B 2 = 1 2 0 0 2 + 2 7 0 0 0 + 1 0 3 0 2 = 16 2 3 2 . 14 ) (a) True. If A is m × n and A 2 is defined we must have n = m so A is square. (b) False. See problem 1 of this assignement. (c) True. If A is m × n then for AB to be defined we must have B is n × p . But for BA to be defined we must have p = m so A is m × n and B is n × m so AB and BA are, respectively...
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 '05
 HUI
 Math, Linear Algebra, Algebra, Harshad number

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