MATH-205 Midterm: Bates MATH 205 111309jayawant205exam
Document Summary
Check that you have 7 questions on four pages. Show all your work to receive full credit for a problem: (10 points) short answers: (show all the calculations needed to get the answers. No explana- tions needed. ) (a) suppose b is a 2 x 2 matrix and ii is an eigenvector of b corresponding to the eigenvalue. Find all the eigenvalues of a. (c) let ~u = Find a vector of length 7 in the direction of the vector ~u. (d) compute the orthogonal projection of (cid:20) 3. 1 (cid:21) onto the line through (cid:20) 3. 4 (cid:21) and the origin: (9 points) let a = Find the coordinates of ~x with respect to the basis you found in part: (7 points) let b = . If so, nd a basis for the corresponding eigenspace. If not, explain why not. (b) is why not. What is the smallest possible dimension of nul.
