exam4 - M340L Second Midterm Exam April 8 2010 1 The...

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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 row-equivalent. 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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exam4 - M340L Second Midterm Exam April 8 2010 1 The...

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