# Week1 - ECON 117 Mathematical Economics Spring 2008 Week 1...

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ECON 117 Spring 2008 Mathematical Economics Week 1 I. The Basics on Sets and Real Functions 1. Vectors (a) Denote in the following X-Y space. () 1,1 = a x y (b) Denote in the above diagram. 2 a Page 1 of 6

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ECON 117 Spring 2008 Mathematical Economics (c) Find () 2,1 , 1,2 . == ab + and draw it. (d) How about ? (e) Find 5,0 , 0,5 . ( ) 1 λλ +− ⋅ , where λ \ . Def): A linear combination of two vectors (narrow meaning) , 12 ,,, n n aa a =∈ a …\ ( ) n n bb b b Then, ( ) ( ) 11 , , 1 n a ⋅+ − ⋅= + − " n b is a linear combination of and b . a Page 2 of 6
ECON 117 Spring 2008 Mathematical Economics (f) How about , where () 1 λλ ⋅+ − ⋅ ab 01 λ ? (g) Find ()( 1, 0, 0 , 0,1,1 . == ) ( ) 1 +− ⋅ , where . Page 3 of 6

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ECON 117 Spring 2008 Mathematical Economics 2. Sets (Definition) A set is a collection of distinct objects. The objects in a set are called the members or elements of the set. (Notations) 1) is a set and A x is a member of . Then, we denote A x A . 2) If set A has no member, we call it an empty set and denote { } A = or A = ∅ .
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Week1 - ECON 117 Mathematical Economics Spring 2008 Week 1...

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