MATH-205 Midterm: Bates MATH 205 041007greer205exam
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Your grade is based on correctness, completeness, and clarity on each exercise. You may use a calculator and the agreed-upon page of notes, but no books or other students. True or false: a least-squares solution of ax = b is a vector x such that kb axk kb a xk for all x in rn. If it is false, correct the statement to make it true. b. ) (10 pts. ) While boiling a pot of water, you take the temperature every two minutes. This generates the data points (0, 15), (2, 37), (4, 68), (6, 89), where the rst coordinate is time, in minutes, and the second coordinate is temperature, in degrees celsius. Using linear algebra techniques, nd the equation y = 0 + 1 x of the least-squares line that best ts these data points. If so, explain why; if not, explain why not. b. ) (5 pts. ) Suppose both u and v are orthogonal matrices.
