quiz 6.5 answers

Linear Algebra with Applications

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Math 20F - Linear Algebra - Winter 2003 Quiz # 6 1 2 Answers — March 4 1. Consider the following table of data values. x -1 0 1 2 y 0424 Find the best linear least squares fit to the data. That is, find the linear function f ( x )= c 0 + c 1 x that best fits the data in the least squares sense. ANSWER: Let A = 1 - 1 10 11 12 and b = 0 4 2 4 . We need to solve A c 0 c 1 · = b . To do this, we solve A T A x = A T b .N o w , A T A = ± 42 26 , and A T b = ( 10 10 ) , so we use row operations: ± 10 10 ± 21 5 13 5 ± 5 5 ± 5 0 - 5 - 5 Solving by backsubstitution gives c 1 =1 and c 0 =2 . So the answer is: f ( x )=2+ x . 2. Let u 1 =(1 , 1 , 1) T and u 2 , - 1 , 0) T . Are these vectors orthogonal? Orthonormal? Let
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