Question: Let R + n = { x = ( x 1 , . . . . , x n ) | x 1 0 ,

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.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

9/14/10 12:39 PM Page 381 Chapter dug84356_ch06a.qxd 6 Rational Expressions Advanced technical developments have made sports equipment faster, lighter, and more responsive to the human body. Behind...

Q:

Exponential fun 7. Extra credit: Exponential Fun (0 points) Since a mod m = a (mod m), we know that we can reduce the base of an exponent modulo m : ak = (a mod m (mod m). But the same is not true of...

Q:

Homework: Hw 10.2 Question 5, 10.2.6 HW Score: 6.36%, 2.1 of 33 points O Points: 0 of 1 Save Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements...

Q:

answer each part surjective functions (= onto) Let f: A - B be a function. 1. Complete the definition: f is called surjective if VBEB .... 2. Consider the function f: R- R defined by f (x) = 3x+ 2. ;...

Q:

# 2 Let f (t ) be the temperature (in degrees Celsius) of a liquid at time t (in hours). The rate of temperature change at time t is determined from f '(t ) . Explain the method of a) solution toeach...

Q:

To solve a rational inequality, we factor the numerator and the denominator into irreducible factors. The cut points are the real ---Select-- V| of the numerator and the real ---Select--- V of the...

Q:

Let P n (x) be the degree n polynomial that interpolates the function f(x) at the pairwise distinct nodes n x i o 1in+1 , written in Newtons form part a and b code and test result please 01. Let P,...

Q:

MAT102 PROOF Example 2. Let S = 2a + 1 : a, be Z, b / 0). Is S a field under usual addition and multiplication? Example 3. Let A = R \\ (2, -2. }, -}}. Is A a field under usual addition and...

Q:

Show that there is a homeomorphism (D^n D^n )/ S^n where the two disks are glued along their boundaries, i.e., the equivalence relation is generated by x^(1) x^(2) for all x D^n with x = 1. Here the...

Q:

In this lab, youll be writing several functions that perform operations on Boolean matrices. Well use 2D lists (lists of lists) in Python to represent matrices. For example, the matrix 0 0 ?? =[1 1 0...

Q:

What is the variance on the portfolio above? What is the standard deviation on the portfolio above? Stock A Stock B Stock C Correlation (A,B) Correlation (A,C) Correlation (B,C) Expected Return...

Q:

The scalar function div(grad 1) = f (also written 2f) is called the Laplacian, and a function f satisfying 2f = 0 is said to be harmonic, concepts important in physics. Show that 2f = fxx + fyy +...

Q:

QUESTION 9 Rohit, an Indian, is a marketing executive in an American company. He graduated from a top Ivy League university in the United States at performance, positive attitude, and innovative...

Q:

Why are people still arguing about the causes of the great financial crisis of 2007-08?