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Unformatted text preview: Math 2940 – Practice problems for final – Dec 2009 On the final exam : The formula sheet on the last page will not be present. Instead, you may bring into the exam one 2sided, 8.5 by 11 inch sheet of paper, that you have written yourself. 1. Let A = 1 2 1 3 3 2 4 1 4 8 2 6 5 (a) Find a basis for the image of A . (b) Find a basis for the kernel of A . (c) What is the rank of A ? 2. Consider the linear space C [ 1 , 1] with inner product defined by < f,g > = Z 1 1 f ( t ) g ( t ) dt. (a) Compute the lengths of the functions f 1 ( t ) = e t , and f 2 ( t ) = e t . (b) Are f 1 ( t ) and f 2 ( t ) orthogonal? Justify your answer. (c) Find the best least squares approximation to the constant func tion g ( t ) = 1 on [ 1 , 1] by a function of the form c 1 f 1 ( t )+ c 2 f 2 ( t ), where c 1 and c 2 are real numbers. 3. Let V be the subspace of P 3 consisting of all f ( t ) such that f (1) = 0 and f (1) = 0 ....
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This note was uploaded on 12/25/2009 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell University (Engineering School).
 Spring '06
 PANTANO
 Math, Multivariable Calculus

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