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MATH 330 Q4445sol

# MATH 330 Q4445sol - Math 330 Quiz 4.4 and 4.5 Quiz 4.4 In...

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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 0 1 0 , vector b 3 = 0 1 0 - 1 , vector b 4 = 1 0 0 - 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 0 1 2 1 0 1 0 4 1 1 0 0 6 1 0 - 1 - 1 8 ( R 2 ,R 3 ,R 4) ( R 2 ,R 3 ,R 4) - R 1 = 1 - 1 0 1 2 0 1 1 - 1 2 0 2 0 - 1 4 0 1 - 1 - 2 6 ( R 3 ,R 4) ( R 3 - 2 R 2 ,R 4 - R 2) = 1 - 1 0 1 2 0 1 1 - 1 2 0 0 - 2 1 0 0 0 - 2 - 1 4 R 4 R 4 - R 3 = 1 - 1 0

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