Prove that for every \bar{S}\in S^n_{++} and for every \alpha \in R_{++} the sets \{ X \in S^n_{+} : \leq \alpha\} \\ and \\ \{ X \in S^n_{+} : = \alpha\}\\ are non-empty convex and compact. also,...

Prove that for every \bar{S}\in S^n_{++} and for every \alpha \in R_{++} the sets \{ X \in S^n_{+} : <\bar{s}, x=""> \leq \alpha\} \\ and \\ \{ X \in S^n_{+} : <\bar{s}, x=""> = \alpha\}\\ are non-empty convex and compact. also, prove that the interior of the first set is non-empty.Prove that for everyS2Sn++and for every2R++the sets