I need the answer as soon as possible 3.For a nonempty set S C R" and a positive real number r ER (and r > 0),define the set rS as follows:rS := {z € R" | z = rx, x E S}.Here rx is the multiplication of the vector x E R" by the scalarre R; in your morefamiliar notation, rã. The set rS is the set of all points that are obtained by multiplyingr with the vectors x E S.For a given nomempty set SC R" and a given positive number r > 0, prove that if S isa convex set then rS is a convex set as well.

Answered: Image /qna-images/answer/67abb2ca-6153-4b09-9bdc-79d978046301.jpg

Answered: define the set rS as follows: rS := {z…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 6E: 6. For the given subsets and of Z, let and determine whether is onto and whether it is...

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Mickey Mantle played for the New York Yankees for 18 years from 1951 to 1968. Year by year he hit the following numbers of home runs: 13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18. We represent these as a vector x in R by making the following assignmemt: x <-c(13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18) Define the vector y by the assignment y <- cumsum(x) Define the variable w using the assignment W <-714-y Define z with the assignment z <-c(X,Y,W) x, y, w and z are vectors. Answer the following using R code. a) Calculate the minimum value of z. b) Calculate the sum of the squares of the elements in z. c) Calculate the sample mean of z. [ d) Calculate the sample variance of z. e) Calculate the sample standard deviation of z f) What is the 18th element of w? (value of w[18]) g) Calculate the sample variance of x. h) Calculate the sample variance of 5*x| i) What is the length(# of elements) in 5*x j) How many unique(different) values…
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