08bAss1

# 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 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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