Homework 3 Solutions - Engineering Math Homework 3...

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Engineering Math Homework 3 Solutions Spring 2010 A œ $# ! " ! #!! $' # $ # % ! % Ô× ÖÙ ÕØ (1) det (do a cofactor expansion across row 2) $ # ! " !# ! ! # $ # % ! %  - - - - (do a cofactor expansion across column 2) œÐ# Ñ ! $ # ! %  - - - - ââ œ Ð#  ÑÐ#  Ñ # %  -- - - ºº œ Ð#  ÑÐ#  Ñ Ð$  ÑÐ%  Ñ  # œ Ð#  ÑÐ#  ÑÐ  (  "!Ñ - - ’“ # œÐ# ÑÐ# ÑÐ #ÑÐ &Ñœ! œ# ß# ß& - (multiplicity ) (multiplicity ) "# $ œ& " (2) Find a basis for the eigenspace of corresponding to : A - " Ô × Ô × Ö Ù Ö Ù Ö Ù Ö Ù Õ Ø Õ Ø ! "A ! ! !!! B ! ! $C ! # % ! # D ! œ Ô × Ö Ù Ö Ù Õ Ø " # ! "ã! "#! ! !!!ã ! ! ! !!ã ! $ ' ! $ã! !!! ! ã! # % !#ã ! ! ! ! Ä A#BDœ!
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Ô × Ô × Ô × Ô×Ô× Ô × Ô× Ô× Ö Ù Ö Ù Ö Ù ÖÙÖÙ Ö Ù ÖÙ ÖÙ Õ Ø Õ Ø Õ Ø ÕØÕØ Õ Ø ÕØ ÕØ A #B  D #B ! D # ! " BB B ! ! " ! ! CC ! C ! ! " ! DD ! ! D ! ! " œœ œ B C D basis: Ô ×Ô×Ô× Ö ÙÖÙÖÙ Õ ØÕØÕØ #!" "! ! !" ! !! " ßß Find a basis for the eigenspace of corresponding to : A - " œ& Ô× Ô × Ô × ÖÙ Ö Ù Ö Ù
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Homework 3 Solutions - Engineering Math Homework 3...

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