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Unformatted text preview: Math 330  Quiz 4.4 and 4.5 3/25/2009 Quiz 4.4 In the following both answers are vectors whose coordinates are all integers. Consider the following basis for R 4 : B = vector b 1 = 1 1 1 1 , vector b 2 =  1 1 , vector b 3 = 1 1 , vector b 4 = 1 1 1. 5 points Let vectorx = 2 4 6 8 Find [ vectorx ] B . SOLUTION: We have to express vectorx as a linear combination of the vector b i . This is nothing more than the solution of the following augmented system: 1 1 1 2 1 1 4 1 1 6 1 1 1 8 ( R 2 ,R 3 ,R 4) ( R 2 ,R 3 ,R 4) R 1 = 1 1 1 2 1 1 1 2 2 1 4 1 1 2 6 ( R 3 ,R 4) ( R 3 2 R 2 ,R 4 R 2) = 1 1 1 2...
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This note was uploaded on 09/19/2009 for the course MATH 330 taught by Professor Johnson,j during the Spring '08 term at Nevada.
 Spring '08
 Johnson,J
 Math, Linear Algebra, Algebra, Vectors, Integers

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