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Spring 2003 - Buss' Class - Quiz 5.5

Spring 2003 - Buss' Class - Quiz 5.5 - Name Student ID...

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Name: Thursday section time: Student ID: Math 20F - Linear Algebra - Spring 2003 Answers to Self-assessment Quiz #5.5 — May 22 You must show your work in order to get credit for a problem. Label your answers clearly. 1. Let u 1 = (1 , 1 , 1 , 0) T and u 2 = (0 , 1 , 1 , 1) T . Let U = Span ( u 1 , u 2 ). Find a basis for U . ANSWER: Form the matrix A = 1 1 1 0 0 1 1 1 . The nullspace of the matrix is equal to U , since R ( A T ) = U . After finding also solutions to A x = 0 (details of work omitted), we have U = Span ((1 , - 1 , 0 , 1) T , (0 , 1 , - 1 , 0) T ) . 2 Find the linear function that best approximates data x -2 0 1 2 y 2 0 1 2 in the least squares sense.
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