2.4 - Math 2940 Solutions, Fall 2011 Section 2 . 4 1 )...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Page1 / 2

2.4 - Math 2940 Solutions, Fall 2011 Section 2 . 4 1 )...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online