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Unformatted text preview: 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...
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This note was uploaded on 02/06/2011 for the course ESM 3A taught by Professor Prof. dr. peter oswald during the Spring '11 term at Jacobs University Bremen.
- Spring '11
- Prof. Dr. Peter Oswald