MATH-205 Midterm: Bates MATH 205 040814ross205exam
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1 and label its columns a1, a2 and a3. Explain why the matrix equation ax = d is inconsistent. Since d is not in col a, nd the least squares solutions to ax = d. show all matrices involved. From the answer to 1b, you can determine the projection vector w of d onto col a. Explain how you can tell that the vectors a1 and a2 form a basis of col a. It turns out that a2 and a3 also form a basis for col a; you don"t need to show this. C = {a2, a3} is an orthogonal basis. Since c is an orthogonal basis, there"s a formula using dot products that you can use to nd the projection vector w of d onto col a. Give that formula and evaluate it (show all the work) and verify it produces the same projection vector w as in 1c. Find the distance from d to col a.
