Fall 2004 - Musat's Class - Practice Exam 2

Fall 2004 - Musat's Class - Practice Exam 2 - 1 PRACTICE...

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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 )) . b ) Find dim(Nul( A )) . Problem 4: Let P 2 denote the set of all polynomials p of degree 2.
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2 a ) Show that H = { p ∈ P 2 : p (0) = 0 } is a subspace of P 2 . b
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Fall 2004 - Musat's Class - Practice Exam 2 - 1 PRACTICE...

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