UCSF 137 Lecture 19: UCSF 137 - Lecture 19 (4)

10. Which of the following is a one-dimensional subspace of R3? A) {(2, y, z)?|x2 – y + 2z=0}. B) {(x,y, 2)7|x + 24 +32 =0}. C) The solution set of Av = 0 where A= 1 -2 3 -1 4 0 0 2 3 D) {(x, y, z)?|x + 2y + 32 = 4}. E) The solution set of Av = 0 where A= 1 0 2 0 2 0 11 0 5

7. Suppose that 4 and -2 are the only eigenvalues of the matrix A. Which of the following statements is true? (a) 41-A is invertible, and there is a nontrivial solution to Av = -2v. (b) det (41+ A) = det(21 - A) = 0. (c) 41 - A is not invertible, and there is a nontrivial solution to Av = -2v. (d) det(41+ A) = 0, and there is a nontrivial solution to (21 - A)v = 0. (e) none of the above

The structure of NH3 the molecule is approximately that of anequilateral tetrahedron, with three H+ ions forming the base and anN3- ion at the apex of the tetrahedron. The length of each side is1.64 x10-10 m. Calculate the electric force that acts on each ion.(Let the H+ ions be in the x-y plane with H1 at (0, 0, 0), H2 at(a, 0, 0), and H3 at (a/2, av(3)/2, 0).The N3- ion, with charge q4in our notation, is then at (a/2, a/2v(3), av(2/3)), where a = 1.64x10-10 m. To simplify our calculations we'll set ke2/a2 = C = 8.56x10-9 N. Use the following variable as necessary : C.)
*need to find the force on each electron (F1, F2, F3, and F4)*