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Find bases for the following subspaces of F5 : Wi = {(ai,a2,a 3 ,a4,a 5 ) F5 : ax - a 3

Chapter 1, Problem 14

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QUESTION:

Find bases for the following subspaces of F5 : Wi = {(ai,a2,a 3 ,a4,a 5 ) F5 : ax - a 3 - a4 = 0} and W2 = {(ai, a 2 , a3, a 4 , a 5 ) F5 : a2 = a 3 = a4 and ax 4- a 5 = 0}. What are the dimensions of Wi and W2?

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QUESTION:

Find bases for the following subspaces of F5 : Wi = {(ai,a2,a 3 ,a4,a 5 ) F5 : ax - a 3 - a4 = 0} and W2 = {(ai, a 2 , a3, a 4 , a 5 ) F5 : a2 = a 3 = a4 and ax 4- a 5 = 0}. What are the dimensions of Wi and W2?

ANSWER:

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Given that,

 

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