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midterm09

# midterm09 - Midterm Examination MAE 107 Sp09(Open book and...

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Midterm Examination MAE 107 Sp09 (Open book and notes. No laptop computers or communication devices are allowed.) 1 1.) (25 %) Given the matrix: A = 1 2 3 6 5 4 7 8 9 a.) write down a single-line Matlab command that will generate the matrix as a Matlab variable A: b.) Write down the numerical answers, if any , that will be given in the Matlab Command Window by the subsequent commands: a.) x=A(:, 3) b.) y=A(2, :) c.) A*ones(3,1) d.) x*y e.) y*x f.) x=1:4 g.) A*x 0 h.) I=eye(3) i.) y=I(:,3) j.) A*y 1 You may use textbook, lecture notes, and handout materials, as well as copies library material from any library in the San Diego area, but not checked-out materials. Please use a blue book or else put your name and PID on each page of your solution. If you use a hand-held calculator, write down all steps performed in the calculation.

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2.) (25 %) Given a matrix of the form A = 1 e f 5 c d 10 a b find the matrix A (1) = M (1) P (1) obtained by the first step in row echelon reduction based on Gaussian elimination with pivoting. Here, M (1) and P (1) are the row combination (shear) and permutation discussed in HW 02 (but you do not need to use the forms for these given in HW 02). 3.) (25 %) In Problem 3 of JDG-NA03, matching of first derivatives at knots gives the following equations for the coefficients a j a 4 ,j
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