[2.25] Show that C= {x : Ax <0}, where A is an m × n matrix, has at most one extreme point, the origin.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
2.25 and 2.26
![•[2.25] Show that C = {x : Ax<0}, where A is an m x n matrix, has at most one
extreme point, the origin.
(2.26] Let S be a simplex in R" with vertices X1, X2,..., Xk+1. Show that the
extreme points of S consist of its vertices.
-12.27] Let S = {x: +2x2 s 4}. Find the extreme points and directions of S.
Can you represent any point in S as a convex combination of its extreme points
plus a nonnegative linear combination of its extreme directions? If not, discuss
in relation to Theorem 2.6.7.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2bc18e7a-f663-40e4-87af-7c08d362e011%2F0dca5614-7405-4401-844b-3d98d8f345f9%2Ft78o39o_processed.png&w=3840&q=75)
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