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Unformatted text preview: CS 205a Fall 2011 Midterm 1 Please write your name on the top right of this page. The exam is closed book/closed notes and no calculators are allowed. You have 1 hour and 15 minutes to complete the exam. Multiple Choice (4 x 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 matrices are always diagonalizable (i.e. the matrices that always have a full set of eigenvectors)? (a) Symmetric matrices (b) Orthogonal matrices (c) Householder matrices (d) Upper triangular matrices 2. Which of the following computations have operation counts of O ( n 3 )? Consider the cases for general n n matrices. (a) QR factorization with the Gram-Schmidt method (b) LU decomposition (c) Back substitution step in solving A~x = ~ b (d) Cholesky factorization 3. k ~x k is best for evaluating the numerical solution to a system of equations A~x = ~ b because: (a) It is often the only obtainable norm...
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- Fall '07