MATH-205 Midterm: Bates MATH 205 032312webster205exam
Document Summary
You must show all work to receive credit. No electronic devices other than calculators are permitted. Give exact answers (such as ln 5 or e2) unless requested otherwise: let k be the set of 3 3 skew-symmetric matrices. Skew-symmetric matrices satisfy a = at . (a) give three examples of 3 3 matrices in k. (b) show that k is a vector space. You may use the fact that all 3 3 matrices form a vector space. (c) find a basis for k: recall from calculus that sin x = We may apply this formally to n n matrices to de ne sin a = Hint: diagonalize a: according to kepler"s rst law, a comet should have an elliptic, parabolic, or hyperbolic orbit. In suitable polar coordinates, the position (r, ) of a comet satis es an equation of the form r = + e(r cos ) where is a constant and e is the eccentricity of the orbit.
