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math34600spring2006

# math34600spring2006 - Department of Mathematics Mathematics...

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Department of Mathematics The City College of New York Mathematics 34600 Final Examination Spring 2006 PART I: Answer any 5 out of 7 questions. Each is worth 16 points. 1. Solve the system of equations. 5 16 11 12 2 2 7 3 1 4 2 4 3 2 1 4 3 2 1 4 3 2 1 = = + + + = + x x x x x x x x x x x x 2. a) Find the inverse of = 4 5 2 3 0 1 1 4 3 A b) Use the answer to part a) to solve the system 1 4 5 2 0 3 1 4 3 3 2 1 3 1 3 2 1 = + = + = + x x x x x x x x 3. a) Determine whether W is a subspace of M + = real b a b b a b a a , : 3 2 2,2 . b) Find a basis for the subspace of R 4 spanned by the vectors v , , , v . () 0 , 0 , 1 , 1 1 = () 1 , 1 , 0 , 0 2 = v () 2 , 2 , 0 , 2 3 = v () 3 , 0 , 3 , 0 4 = 4. Let A = 1 1 1 0 1 2 3 1 1 1 2 3 a) Find a basis for the nullspace of A . b) Find a basis for the column space of

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math34600spring2006 - Department of Mathematics Mathematics...

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