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# Question about Vector Spaces... watch

1. Let W be the set of all vectors of the form shown, where a, b, and c represent arbitrary real numbers. Either find a set S of vecors that spans W or give an example to show that W is NOT a vector space.

W = [4a+3b ; 0 ; a+b+c ; c-2a]

W is supposed to be a 4x1 matrix but I couldn't type it as a matrix...

This is how I did it (again, these are all 4x1 matrices):

a[ 4 ; 0 ; 1 ; -2 ] + b[3 ; 0 ; 1 ; 0] + c[0 ; 0 ; 1 ; 1]
So W is a vector space...is my answer correct?

2. you're close. the set S consists of those 3 vectors *separately*, instead of summed together with a,b,c factors.

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