08bAss2 - AS2/MATH1111/YKL/08-09 THE UNIVERSITY OF HONG...

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AS2/MATH1111/YKL/08-09 THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1111: Linear Algebra Assignment 2 Due date : Feb 19, 2009 before 6:30 p.m. Where to hand-in : Assignment Box outside the lifts on the 4th floor of Run Run Shaw Remember to write down your Name , Uni. no. and Tutorial Group number . If you find difficulties, you are welcome to see the instructor, tutors or seek help from the help room. See “Information” at http://147.8.101.93/MATH1111/ for availabilities. Any discovered plagiarism will be referred to University Disciplinary Committee. 1. (a) Apply the type II and type III elementary row operations (i.e. no interchange of rows) to reduce A = 2 - 6 - 2 - 1 3 3 - 1 3 7 into row echelon form. (b) Hence find a lower triangular matrix L and an upper triangular matrix U such that A = LU . [See p.67 of textbook for the definition of upper and lower triangular matrices.] 2. Let A = ( a ij ) n × n be a square matrix of order n . The trace of A , denoted by tr( A ), is defined as tr( A ) = n X i =1 a ii = a 11 + a 22 + · · · + a nn .
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