- #1
bonildo
- 14
- 1
This exercise is located in the vector space chapter of my book that's why I am posting it here.
Recently started with this kind of exercise, proof like exercises and I am a little bit lost
Proof that given a, b, c real numbers, the set X = {(x, y) E R^2; ax + by <= c} ´is convex at R^2
the definition of convex set in the book is given like that: u, v E X => [u, v] C X
and [u,v]={ (1-t)u+tv ; 0<=t<=1}Didnt do much, just that :
u=(x1,y1) and ax1+by1<c
v=(x2,y2) and ax2+by2<c
and that [u,v]={(1-t)x1+tx2,(1-t)y1+ty2)}
Recently started with this kind of exercise, proof like exercises and I am a little bit lost
Proof that given a, b, c real numbers, the set X = {(x, y) E R^2; ax + by <= c} ´is convex at R^2
the definition of convex set in the book is given like that: u, v E X => [u, v] C X
and [u,v]={ (1-t)u+tv ; 0<=t<=1}Didnt do much, just that :
u=(x1,y1) and ax1+by1<c
v=(x2,y2) and ax2+by2<c
and that [u,v]={(1-t)x1+tx2,(1-t)y1+ty2)}