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3. LINEARLY INDEPENDENCY 17 Solution Choose t 1 = - 1 , t 2 = 0 , and t 3 = 1 , f 1 (t 1 ) f 1 ( t 2 ) f 1 ( t 3 ) f 2 ( t 1 ) f 2 ( t 2 ) f 2 ( t 3 ) f 3 ( t 1 ) f 3 ( t 2 ) f 3 ( t 3 ) = 7 3 2 1 - 6 - 9 20 4 - 2 Compute the determinant, 7 3 2 1 - 6 - 9 20 4 - 2 = 50 , so the functions are linearly independent. a Project At beginning you should enter: Project title, your name, ss#, and due date in the following format Project One: Define and Graph Functions John Doe SS# 000-00-0000 Due: Mon. Nov. 23rd, 2003 You should format the text region so that the color of text is different than math expression. You can choose color for text from Format– > Style select normal and click modify , then change the settings for
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Unformatted text preview: font. You can do this for headings etc. (1) Independent of functions as vectors Goal: Familiar your self with the concept of linearly indepen-dency. • Use the Mathcad code provided at at the website www.unf.edu/ ∼ mzhan /linear i n to check if given set of functions are linearly independent or not. { sin( x ) , sin(2 x ) , sin(3 x ) } { t 2 , 2 t 2-2 t + 4 , 3 t, 6 } { e t ,te t ,t 3 e t } { e 2 t ,e t ,e 3 t } • Using algebraic arguments or reasoning to verify the con-clusion of the Mathcad code....
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This note was uploaded on 10/04/2011 for the course MAP 4231 taught by Professor Dr.han during the Spring '11 term at UNF.

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