Linear Algebra Consider the following subset W of the given vector spaces V . (i) Find two nonzero (non-trivial) elements in W and justify why they belong to W. (ii) Determine whether W is a subspace...

Linear Algebra

Consider the following subset W of the given vector spaces V .

(i) Find two nonzero (non-trivial) elements in W and justify why they belong to W.

(ii) Determine whether W is a subspace of V . Give proof if it is, or a counter example if it is not.

 V =R^3, W = {(x_1,x_2,x_3) ∈ R^3 | x_1 ≤ x_2 ≤ x_3}

where R is the set of all real numbers