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3f-fall2010-homework12solutions

# 3f-fall2010-homework12solutions - Math 3F Homework#12...

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Math 3F — Homework #12 Solutions 1. If A = 1 - 2 0 3 2 - 1 2 1 3 and B = 4 - 2 3 - 1 5 0 6 1 2 , compute: (a) 2 A + B 2 A + B = 2 1 - 2 0 3 2 - 1 2 1 3 + 4 - 2 3 - 1 5 0 6 1 2 = 2 - 4 0 6 4 - 2 4 2 6 + 4 - 2 3 - 1 5 0 6 1 2 = 6 - 6 3 5 9 - 2 10 3 8 . (b) A - 4 B A - 4 B = 1 - 2 0 3 2 - 1 2 1 3 - 4 4 - 2 3 - 1 5 0 6 1 2 = 1 - 2 0 3 2 - 1 2 1 3 - 16 - 8 12 - 4 20 0 24 4 8 = - 15 6 - 12 7 - 18 - 1 - 22 - 3 - 5 . (c) AB AB = 1 - 2 0 3 2 - 1 2 1 3 4 - 2 3 - 1 5 0 6 1 2 = 6 - 12 3 4 3 7 25 4 12 . (d) BA BA = 4 - 2 3 - 1 5 0 6 1 2 1 - 2 0 3 2 - 1 2 1 3 = 4 - 9 11 14 12 - 5 13 - 8 5 .

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2. If A = ( 1 + i - 1 + 3 i 3 + 2 i 2 - i ) and B = ( i 3 2 - 2 i ) , find: (a) A - 2 B A - 2 B = ( 1 + i - 1 + 3 i 3 + 2 i 2 - i ) - 2 ( i 3 2 - 2 i ) = ( 1 + i - 1 + 3 i 3 + 2 i 2 - i ) - ( 2 i 6 4 - 4 i ) = ( 1 - i - 7 + 3 i - 1 + 2 i 2 + 3 i ) . (b) 3 A + B 3 A + B = 3 ( 1 + i - 1 + 3 i 3 + 2 i 2 - i ) + ( i 3 2 - 2 i ) = ( 3 + 3 i - 3 + 9 i 9 + 6 i 6 - 3 i ) + ( i 3 2 - 2 i ) = ( 3 + 4 i 9 i 11 + 6 i 6 - 5 i ) .
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3f-fall2010-homework12solutions - Math 3F Homework#12...

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