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# mt1C-sol - Midterm 1 CS 257 Group C March 1 2005 Time...

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Midterm 1, CS 257 Group C March 1, 2005 Time: 9:45AM-10:45AM Name: . NetID: . Signature: . No book or notes 9 Questions, 9 pages: (125 points) All questions are 10 points, unless otherwise stated. 1. What does the MATLAB command eye(3)-ones(3) return? 1 0 0 0 1 0 0 0 1 - 1 1 1 1 1 1 1 1 1 = 0 - 1 - 1 - 1 0 - 1 - 1 - 1 0 1

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2. For A = [8 7; 6 5; 4 3; 2 1] and b = [1; 2; 3; 4] , complete the following MATLAB code to obtain the vector x that minimizes min x A x - b 2 [s,t]= qr(A) x = t\(s’*b) 2
3. (15 points) Without using the LU factorization, determine the inverse of: L = 1 0 0 0 3 1 0 0 0 3 1 0 0 0 3 1 Show your work. L = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 - 0 0 0 0 - 3 0 0 0 0 - 3 0 0 0 0 - 3 0 L - 1 = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 + 0 0 0 0 - 3 0 0 0 0 - 3 0 0 0 0 - 3 0 + 0 0 0 0 - 3 0 0 0 0 - 3 0 0 0 0 - 3 0 2 + 0 0 0 0 - 3 0 0 0 0 - 3 0 0 0 0 - 3 0 3 L - 1 = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 + 0 0 0 0 - 3 0 0 0 0 - 3 0 0 0 0 - 3 0 + 0 0 0 0 0 0 0 0 9 0 0 0 0 9 0 0 + 0 0 0 0 0 0 0 0 0 0 0 0 - 27 0 0 0 L - 1 =

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mt1C-sol - Midterm 1 CS 257 Group C March 1 2005 Time...

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