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?
Thank you in advance.
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- Thread Starter
- 19-03-2011 12:09
- 19-03-2011 13:48
you're close. the set S consists of those 3 vectors *separately*, instead of summed together with a,b,c factors.