MATH-205 Midterm: Bates MATH 205 041504ross205exam
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1a) the three points (1, 5), (2, 3), and (3, 5) all lie on one parabola of the form y = a + bx + cx2. 1b) write the above system in augmented matrix form, and proceed to put that matrix in row- reduced echelon form. Show all steps, including any multiplications involving matrix transposes. 3c) find the least-squares solutions of ax = b. The answer works out nicely, so be careful. 3d) find both the projection p of b onto col(a) and the vector z col(a)) such that b = p+z. 3e) explain why nding a basis for col(a)) is the same as nding a basis for null(col(at )). Hint: col(a)) consists of all vectors v which are to all the column vectors of a. That means c v=0 for each column c of a. Columns of a turn into rows of at . Explain why the columns of a form an orthogonal set.
