(a) Define vector space and determine whether the set of all positive real numbers u with...

 

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(a) Define vector space and determine whether the set of all positive real numbers u with the operations uev = 2u – v and cou = cu is a vector space? (b) Express i = (3,7,-4) as a linear combination of i = (1,2,3), y = (2,3,7), z = (3,5,6), also check whether the vectors i, y, ż are linearly dependent or independent? (a) Define vector space and determine whether the set of all positive real numbers u with the operations uev = 2u – v and cou = cu is a vector space? (b) Express i = (3,7,-4) as a linear combination of i = (1,2,3), y = (2,3,7), z = (3,5,6), also check whether the vectors i, y, ż are linearly dependent or independent?