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# ESM3A HW3 - Jacobs University Bremen School of Engineering...

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Jacobs University Bremen School of Engineering and Science Peter Oswald Fall Term 2010 120201 ESM3A — Problem Set 3 Issued: 22.9.2010 Due: Wednesday 29.9.2010 (in class) This homework deals with LU factorization, the concept of orthogonality, Gram-Schmidt orthog- onalization, and QR factorization. Consult the textbook by G. Strang [S] (or any other text on the subject of matrix calculations and linear algebra) and the script [MK] by K. Mallahi-Karai. Do not compute numerical values of square roots, but compute the value of the angle (in radians or degrees) in Problem 3.2 b). 3.1. Find the LU decomposition of A = - 1 2 - 3 4 - 5 2 - 2 4 - 6 8 - 1 4 - 5 6 - 7 and use it to write down the general solution of the homogeneous underdetermined system Ax = 0. 3.2. Let ( · , · ) be the standard inner product on IR n . a) Let a = (1 , 2) T , b = ( - 1 , 1) T R 2 . If c is a vector such that ( a , c ) = - 1 and ( b , c ) = 3, find c . b) Find the angle between the vectors a = (1 , 2 , 2 , 3) T and b = (3 , 1 , 5 , 1) T . By definition, the angle between two non-zero vectors a , b in an Euclidean space V with scalar

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ESM3A HW3 - Jacobs University Bremen School of Engineering...

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