Given W={(x,y,z):xy=z} ...(1)
Recall : A subset is said to be subspace of a vector space if
1) x,y"\\in" W "\\implies" x+y"\\isin" W
2) if x"\\isin" W and a"\\isin" F "\\implies"ax"\\in" W
Now let's check these property for given W
Let x=(x1,y1,z1) and y=(x2,y2,z2) "\\isin" W
Hence , x1y1=z1 and x 2y2=z2
But (x+y)=(x1+x2 ,y1+y2,z1+z2)
So, (x1+x2)(y1+y2)=(z1+z2) is NOT equal to x1y1+x2y2=(z1+z2)
Hence ,(x+y) does not belong to W
Hence W is not a subspace.
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