Determine whether W = {(x, y,z) | x + y + z + 1 = 0, x, y,z ∈ R} a subspace of R³ or
not?
Let "x=y=z=0", then "x+y+z+1=1\\neq0", hence the zero vector "(0,0,0)\\in R^3" is not in "W". Therefore, "W" is not a subspace of "R^3".
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