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Unformatted text preview: M340L Second Midterm Exam, April 8, 2010 1. The matrices A = 1 1 1 1 12 1 2 1 3 2 6 5 37 2 1 1 2 23 and B = 1 2 4 1 3 1 1 7 are rowequivalent. a) Find a basis for Col ( A ). What is dim ( Col ( A ))? b) Find a basis for Nul ( A ). What is dim ( Nul ( A ))? c) Find a basis for Row ( A ). What is dim ( Row ( A ))? d) M 2 , 2 is the space of 2 × 2 matrices. Let V be the subspace of M 2 , 2 spanned by braceleftbiggparenleftbigg 1 1 2 parenrightbigg , parenleftbigg 1 2 1 parenrightbigg , parenleftbigg 1 2 6 1 parenrightbigg , parenleftbigg 1 1 5 2 parenrightbigg , parenleftbigg 12 3 37 23 parenrightbiggbracerightbigg . Find a basis for V . 2. On R 3 , let E be the standard basis and let B = 1 1 1 , 2 3 1 , 1 1 2 ....
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 Spring '08
 PAVLOVIC
 Linear Algebra, characteristic equation, M2,2

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