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Unformatted text preview: CS 205a Fall 2010 Midterm 1 Please write your name on the top right of the first page. The exam is closed book, and no calculators are allowed. You have 1 hour and 15 minutes to complete the exam. Multiple Choice (1 pt each) For each of the following questions, circle all answers which are correct. You must circle all of the answers for a given question correctly to receive credit. 1. Which of the following can be said about a Householder matrix H = I- 2 vv T v T v (a) The condition number for H is 1 (b) It is a projection matrix onto the hyperplane orthogonal to v (c) It preserves the 2-norm of a vector (ie k x k 2 = k Hx k 2 for all x ) (d) One of the eigenvalues of H is 1 with multiplicity n- 1 2. Which of the following classes of matrices are positive semi-definite? (a) Permutation matrices (b) Projection matrices (c) Reflection matrices (d) Symmetric matrices 3. Suppose that a square matrix A is ill-conditioned. Which of the following matrices could potentially have a better condition number?have a better condition number?...
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- Fall '07
- Matrices, pts, Orthogonal matrix, RK, complete orthogonal factorization