MATH-205 Midterm: Bates MATH 205 032008greer205exam
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Your grade is based on correctness, completeness, and clarity on each exercise. You may use a calculator, but no notes, books, or other students. Consider the subset of p2 of all polynomials of the form p(t) = a + bt2, where a is in r and b is in r. demonstrate that this subset is a subspace of p2. b. ) (5 pts. ) Let h be the set of points inside and on a circle of radius 2 that is centered at the origin of the xy plane. That is, h = {(x, y) : x2 + y2 4}. Use an example (two vectors, or a vector and a scalar) to show that h is not a subspace of r2. Use the invertible matrix theorem (imt) to respond to the following questions. Be sure to state clearly which parts of the imt you are using. A is n n. a. ) (5 pts. )
