Explanation Given: The set S of all x that satisfy this inequality a x 1 + b x 2 ≤ c is called a closed half-space of ℝ 2 . Let v = [ a b ] and x = [ x 1 x 2 ] . The inequality a x 1 + b x 2 ≤ c for some real number c may be written as v T x < c . Result used: A set X ⊆ ℝ n is convex if the convex combination of any two points in X is also in X; that is, for all x 1 , x 2 ∈ X , then the point x = α 1 x 1 + α 2 x 2 ⊆ X such that α 1 + α 2 = 1 , α 1 ≥ 0 , α 2 ≥ 0 and for all x 1 ≥ 0 , x 2 ≥ 0 . Calculation: Let v = [ a b ] and x = [ x 1 x 2 ] , satisfy the inequality a x 1 + b x 2 ≤ c for some real number c and it may be written as v T x < c . Let us take the two vectors x 1 = [ x 1 x 2 ] and x 2 = [ y 1 y 2 ] , Hence v T x 1 < c and v T x 2 < c where v = [ a b ]

5th Edition

ISBN: 2818440100055

Author: Lay

Publisher: PEARSON

See similar textbooks

Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

Videos

Question

Chapter 9.2, Problem 17E

To determine

To show: The set S is a convex set in ℝ2 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.2, Problem 16E

Chapter 9.2, Problem 18E

Students have asked these similar questions

(±³d-12) (−7+ d) = |||- \d+84

(z- = (-2) (→ Use the FOIL Method to find (z — · -

MODELING REAL LIFE Your checking account has a constant balance of $500. Let the function $m$ represent the balance of your savings account after $t$ years. The table shows the total balance of the accounts over time. Year, $t$ Total balance 0 1 2 3 4 5 $2500 $2540 $2580.80 $2622.42 $2664.86 $2708.16 a. Write a function $B$ that represents the total balance after $t$ years. Round values to the nearest hundredth, if necessary. $B\left(t\right)=$ Question 2 b. Find $B\left(8\right)$ . About $ a Question 3 Interpret $B\left(8\right)$ . b represents the total balance checking and saving accounts after 8 years the balance would be 16 / 10000 Word Limit16 words written of 10000 allowed Question 4 c. Compare the savings account to the account, You deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly. A = 11998.70 SINCE 9000 is the principal ( 1+0.036/12)12 times 8 gives me aproxtimately 1997 14 / 10000 Word Limit14 words written of 10000 allowed Skip to…

Chapter 9 Solutions

LINEAR ALGEBRA AND ITS APPLICATION -TEX

Ch. 9.1 - Find the optimal strategies and the value of the...Ch. 9.1 - Player R has a supply of dimes and quarters....Ch. 9.1 - Prob. 2E Ch. 9.1 - In the traditional Japanese childrens game janken...Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Find all saddle points for the matrix games in...Ch. 9.1 - Find all saddle points for the matrix games in...Ch. 9.1 - Find all saddle points for the matrix games in...Ch. 9.1 - Prob. 9E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The set S is a convex set in ℝ 2 .

Solution Summary: The author explains that the set S is a convex set in R2.

Concept explainers

Videos

To show: The set S is a convex set in ℝ2 .

Want to see the full answer?

Chapter 9 Solutions