practicemid2_20F_fall04

practicemid2_20F_fall04 - b ) Find dim(Nul( A )) . Problem...

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1 PRACTICE MIDTERM 2 MATH 20F, LECTURE C Directions: Do all the problems. Write your solutions clearly and give explanations for your work. Answers without justifications will not be given credit. Problem 1: Consider the matrices A = 1 - 3 5 - 2 1 6 0 7 0 , B = - 3 0 0 0 1 / 4 0 0 0 2 a ) Compute Rank (A). b ) Compute det( AB - 1 ). Problem 2: Determine whether each of the following sets of vectors is a subspace of R 4 . Justify. a ) H = x y z w : y + w 3 x + 2 z + 1 . b ) W = 2 a - 3 b - 4 a + b b a : a,b scalars . Problem 3: Consider the matrix A = 2 0 1 0 1 0 0 0 - 2 - 1 - 2 0 a ) Find dim(Col( A )) .
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Unformatted text preview: b ) Find dim(Nul( A )) . Problem 4: Let P 2 denote the set of all polynomials p of degree 2. 2 a ) Show that H = { p P 2 : p (0) = 0 } is a subspace of P 2 . b ) What is the dimension of H ? Justify. Problem 5: Let A be a 5 5 matrix with eigenvalues-7 , 3 , 5. Assume that the eigenspace of = 3 has dimension 3. a ) Is A diagonalizable? Justify. b ) Is it possible to nd 2 independent eigenvectors in the eigenspace corresponding to = 5? If yes, give examples, if no, justify....
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This note was uploaded on 04/14/2008 for the course MATH 20F taught by Professor Buss during the Winter '03 term at UCSD.

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practicemid2_20F_fall04 - b ) Find dim(Nul( A )) . Problem...

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