Question

14. For each of the following sets, show whether it is convex or not. (a) ?...

14. For each of the following sets, show whether it is convex or not.

(a) ? = {(?1, ?2 ) ? ∈ ? 2 : ?1 + ?2 ≤ 2, ?1 ≥ 0, ?2 ≥ 0}

(b) ? = {(?1, ?2 ) ? ∈ ? 2 : ?2 − ?1 2 = 0}

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Show by counterexample that the union of two convex sets need not be convex. (A picture...
Show by counterexample that the union of two convex sets need not be convex. (A picture will suffice.) Please write clearly & show all work. Thank you!
Determine whether or not the following sets are perfect and whether or not the following sets...
Determine whether or not the following sets are perfect and whether or not the following sets are connected. Show work. a) [0,7) U (7,10] b) [1,3] U [4,8] c) {1, 1/2, 2/3, 3/4, ...}
For each of the following sets, determine whether they are countable or uncountable (explain your reasoning)....
For each of the following sets, determine whether they are countable or uncountable (explain your reasoning). For countable sets, provide some explicit counting scheme and list the first 20 elements according to your scheme. (a) The set [0, 1]R × [0, 1]R = {(x, y) | x, y ∈ R, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}. (b) The set [0, 1]Q × [0, 1]Q = {(x, y) | x, y ∈ Q, 0 ≤ x ≤...
Exercise 4.11. For each of the following, state whether it is true or false. If true,...
Exercise 4.11. For each of the following, state whether it is true or false. If true, prove. If false, provide a counterexample. (i) Let X and Y be sets from Rn. If X ⊂ Y then X is closed if and only if Y is closed. (ii) Let X and Y be sets from Rn. If X ∩Y is closed and convex then either X or Y is closed and convex (one or the other). (iii) Let X be an...
Show whether the following vectors/functions form linearly independent sets: (a) 2 – 3x, x + 2x^2...
Show whether the following vectors/functions form linearly independent sets: (a) 2 – 3x, x + 2x^2 , – x^2 + x^3 (b) cos x, e^(–ix), 3 sin x (c) (i, 1, 2), (3, i, –2), (–7+i, 1–i, 6+2i)
Decide whether each of the given sets is a group with respect to the indicated operation....
Decide whether each of the given sets is a group with respect to the indicated operation. If it is not a group, state a condition in the definition of group that fails to hold. (a) The set {[1],[3],[5]}⊂Z8 with the operation multiplication. (b) The set {[0],[2],[4],[6],[8]}⊂Z10 with operation addition.
Consider the following sets: ?={112?−59|?∈ℤ}, ?={16?−11|?∈ℤ}, and ?={14?+11|?∈ℤ}. a) Show that ? is a proper subset...
Consider the following sets: ?={112?−59|?∈ℤ}, ?={16?−11|?∈ℤ}, and ?={14?+11|?∈ℤ}. a) Show that ? is a proper subset of ?. b) Show that ? is a proper subset of ?. c) Show that there is no containment relation between ? and ?
Exercise 4.11. For each of the following, state whether it is true or false. If true,...
Exercise 4.11. For each of the following, state whether it is true or false. If true, prove. If false, provide a counterexample. (i) LetX andY besetsfromRn. IfX⊂Y thenX is closed if and only if Y is closed. (ii) Let X and Y be sets from Rn. If X ∩Y is closed and convex then eitherX or Y is closed and convex (one or the other). (iii) LetX beanopensetandY ⊆X. IfY ≠∅,thenY isaconvexset. (iv) SupposeX isanopensetandY isaconvexset. IfX∩Y ⊂X then X∪Y...
About convex function: (1) Please show that f(x) = ax2 + bx + c is a...
About convex function: (1) Please show that f(x) = ax2 + bx + c is a convex function if and only if a ≥ 0. (2) Please show that f(x) = 1/2·xTQx+aTx is a convex function if and only if Q is positive semi-definite.
(c) Compute the sample correlation coefficient r for each of the following data sets and show...
(c) Compute the sample correlation coefficient r for each of the following data sets and show that r is the same for both. (Use 3 decimal places.) (i) x 5 2 9 y 1 2 5 (ii) x 1 2 5 y 5 2 9 r (i) (ii)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT