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 0 4 2 4 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 1 0 1 1 1 2 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 . Now, A T A = 4 2 2 6 , and A T b = ( 10 10 ) , so we use row operations: 4 2 10 2 6 10 2 1 5 1 3 5 1 3 5 2 1 5 1 3 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 , - 1 , 0) T . Are these vectors orthogonal?
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