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Let 1\mathbf{R}_+^{n} = \{ x = (x_1, ., x_n) | x_1 \geq 0, x_2 \geq 0,., x_n \geq 0 } be the nonnegative orthant of \mathbf{R}^n. Proof the following:...

Let R+n={x=(x1,....,xn) | x10,x20,...,xn0 } be the nonnegative orthant of Rn.

Proof the following:

1) Let cRn be given. Show that cTx0 for xR+n if and only if cR+n .

2) Let x,yR+n . Show that xTy=0 if and only if xiyi=0 for each i = 1,....n.

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