08bAss1 - AS1/MATH1111/YKL/08-09 THE UNIVERSITY OF HONG...

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AS1/MATH1111/YKL/08-09 THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1111: Linear Algebra Assignment 1 Due date : Feb 2, 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. We do not count assignment grades in your final score unless you fall in a marginal case. Any discovered plagiarism will be referred to University Disciplinary Committee. 1. Find a , b and c so that the system x + ay + cz = 0 bx + cy - 3 z = 1 ax + 2 y + bz = 5 has the solution x = 3, y = - 1, z = 2. 2. Given two nonzero vectors x 1 = ( a b ) T , x 2 = ( c d ) T R 2 . (a) Suppose that x 1 is not a scalar multiple of x 2 (i.e. x 1 6 = λx 2 for any λ R ). Show that every vector x R 2 is a linear combination of x 1 and x 2 . (b) Will the conclusion remain hold if x 1 is a scalar multiple of x 2 ? Justify your answer. 3. Determine all 2 × 2 nonsingular matrices A that satisfy A 3 =
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