Let $R={x=(x,....,x)$ | $x≥0,x≥0,...,x≥0$ } be the nonnegative orthant of $R.$

Proof the following:

1) Let $c∈R$ be given. Show that $cx≥0$ for $∀x∈R$ if and only if $c∈R$ .

2) Let $x,y∈R$ . Show that $xy=0$ if and only if $xy=0$ for each i = 1,....n.

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