10aAss1

# 10aAss1 - AS1/MATH1111/YKL/10-11 THE UNIVERSITY OF HONG...

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AS1/MATH1111/YKL/10-11 THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1111: Linear Algebra Assignment 1 Due date : Sept 21, 2010 before 6:30 p.m. Where to hand-in : Assignment Box outside the lifts on the 4th ±oor of Run Run Shaw Remember to write down your Name , Uni. no. and Tutorial Group number . ± We do not count assignment grades in your ±nal score, but your e²ort on assignments will be considered in case you are marginally failed. ± You have to learn how to present solutions/proofs logically and clearly . The clarity of presentation counts in tests/examinations. That’s why we read your assignment work. ± If you get di³culties, you are welcome to see the instructor, tutors or seek help from the help room. See \Information" at http://hkumath.hku.hk/course/MATH1111/index.html for availabilities. Part I: Hand-in your solutions 1. Given two nonzero vectors x 1 = ( a b ) T ;x 2 = ( c d ) T 2 R 2 . (a) Suppose that x 1 is not a scalar multiple of x 2 (i.e. x 1 6 = ±x 2 for any ± 2 R ). Show that every vector x 2 R 2 is a linear combination of x 1 and x 2 .

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10aAss1 - AS1/MATH1111/YKL/10-11 THE UNIVERSITY OF HONG...

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