Determine whether the subset S x y z x greaterthanorequalto

Determine whether the subset S = {(x, y, z); x greaterthanorequalto 0} of R^3 is it subspace of R^3.

We have S = {(x , y, z): x 0} . Let be an arbitrary scalar and let (x, y, z) be an arbitrary member of S. Then x 0. Now, (x,y,z) = (x, y, z). Since x 0 when is negative, hence S is not closed under scalar multiplication. Therefore, S is not a subspace of R³.

$Determine whether the subset S = {(x, y, z); x greaterthanorequalto 0} of R^3 is it subspace of R^3.SolutionWe have S = {(x , y, z): x 0} . Let be an arbitrary$

Determine whether the subset S x y z x greaterthanorequalto

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