My Math Forum Convex Hull Problem

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 March 23rd, 2014, 07:57 AM #1 Newbie   Joined: Mar 2014 Posts: 2 Thanks: 0 Convex Hull Problem Hi, Iam new to the forum.....I am B-tech student but week mathematics.....so please help me to solve my problem as soon as possible....... problem is from a previous year question paper. it is from the unit Linear algebra ....it is from the topic convex hull... problem... For a1(6,6) , a2(9,12) , a3(3,9) , with lamda1=1/3 , lamda2=1/3 , lamda3=1/3 (so that lamda1+lamda2+lamda3=1 and all lamda>0 ). Find the convex hull and represent it.
 March 24th, 2014, 12:53 PM #2 Senior Member   Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 Re: Convex Hull Problem Given points $a_1$, $a_2$, $a_3$, the numbers $\lambda_1$, $\lambda_2$, $\lambda_3$ represent a single point with coordinates $\lambda_1a_1+\lambda_2a_2+\lambda_3a_3$. The convex hull of $a_1$, $a_2$, $a_3$ is (the inside of) a triangle with vertices in those points. It can be written as $\{\lambda_1a_1+\lambda_2a_2+\lambda_3a_3\mid \lambda_1,\lambda_2,\lambda_3\ge0, \lambda_1+\lambda_2+\lambda_3=1\}$ I am not sure if this is the representation the problem asks for. Thanks from duc
 March 25th, 2014, 05:00 AM #3 Newbie   Joined: Mar 2014 Posts: 2 Thanks: 0 Re: Convex Hull Problem Thank you for helping me ..........it was given as an assignment for me......
 March 26th, 2014, 07:18 AM #4 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Convex Hull Problem You seem to be a bit confused about your definitions or at least your notation. The "convex hull" of three points in a plane is the triangle having those points as vertices together with its interior. It is true that any point in the convex hull of points P, Q, and R can be written as $\lambda_1P+ \lambda_2Q+ \lambda_2R$ for some numbers $\lambda_1$, $\lambda_2$, and $\lambda_3$ all between 0 and 1 and such that $\lambda_1+ \lambda_2+ \lambda_3= 1$. For the very special case of $\lambda_1= \lambda_2= \lambda_3= \frac{1}{3}$, that point is the centroid of the triangle. Thanks from duc

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### find convex hull of a set of points in linear algebra \lamda=1/3

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