Given points pı = , and p3 in R², P2 let S = conv{pj,P2»P3}. For each linear functional f, find the maximum value m of f on the set S, and find all points x in S at which f(x) = m. a. f(x1,x2) = x1 + x2 b. f(x1,x2) = X1 – X2 c. f(x1,x2) =-2x1 + x2

Given points pı = , and p3 in R², P2 let S = conv{pj,P2»P3}. For each linear functional f, find the maximum value m of f on the set S, and find all points x in S at which f(x) = m. a. f(x1,x2) = x1 + x2 b. f(x1,x2) = X1 – X2 c. f(x1,x2) =-2x1 + x2

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 10EQ

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Question

Given points pı =
, and p3
in R²,
P2
let S = conv{pj,P2»P3}. For each linear functional f, find
the maximum value m of f on the set S, and find all points
x in S at which f(x) = m.
a. f(x1,x2) = x1 + x2
b. f(x1,x2) = X1 – X2
c. f(x1,x2) =-2x1 + x2

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