Question

Let S be a subset of F^{3 }defined as S={(x, y, z)∈F³ :x+y+z=4}.Then determine if S is a subspace of F³ or not

Answer 1

S is not a subspace of F³

The simlest way to see this , it does not contain 0 = (0, 0, 0)

the coordinates (x,y,z) of the zero vector satisfy x+y+z = 0 , $\neq$ 4 as seen