A1 - CO 350 Assignment 1 Fall 2009 Due Friday September 25...

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CO 350 Assignment 1 – Fall 2009 Due: Friday September 25 at 10 a.m. Solutions are due in drop box #6 , outside MC 4066 by the due time: Slot #1 (A-J), Slot #2 (K-S), Slot #3 (T-Z). Section 1: J. Cheriyan, TTh 10-11:20 a.m. Section 2: W.H. Cunningham, MWF 10:30-11:20 a.m. Please acknowledge all outside sources, as well as all collaboration, discussion, help, etc., in your submission. 0. Begin your assignment with the following: Last Name: (Fill in your last name. Please print.) First Name: (Fill in your “official” first name. No nicknames. Please print.) ID: (Fill in your UW student ID) Section: (Fill in your section number) 1. Linear Algebra Review (a) Let S = { v (1) , v (2) , . . . , v ( n ) } be a set of n vectors from a vector space V . Define what it means for S to be a linearly independent set . ( Remark : We are denoting the j th vector in S by v ( j ) ; the parentheses are used to indicate that the superscript is being used for indexing and not for exponentiation.) (b) Let S = { v (1) , v (2) , . . . , v ( n ) } be a set of n vectors from a vector space V . Prove: If the set S is linearly dependent, then there exists a vector in S that can be written as a linear combination of the other vectors in S . (c) Is the set of vectors { ( x 1 , x 2 ) T R 2 | x 2 1 = x 2 2 } a subspace of (the vector space) R 2 ?
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