MATH 330 Q4445sol

MATH 330 Q4445sol - Math 330 - Quiz 4.4 and 4.5 3/25/2009...

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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.

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MATH 330 Q4445sol - Math 330 - Quiz 4.4 and 4.5 3/25/2009...

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