This is exactly the line given in vector form by vex the and t(a- b)b. ang -H l is the vertical line 2 Since a b 7 Let containing b (and a). following subse (d) Anl is the set (a All non-n faã +Bb a, p0 and a +B = 1} Ў. (b) All non-n This is the set of convex linear combina- tions of a and b. (c)) All conve (e)Anl is the line segment with endpoints a and b. (d) All conve (e) All conv The goal of and c 2 6 Let a - 1 - (a) T this question-is to give and justify a drawing of the set of convex linear combinations of a, b, and c. This requires an understanding of the previous question t -} (a)) Let Write as a convex linear combi- (b) nation of a and b. (b) Let ě = Write e as a convex linear combi- (c) nation of c and d. Substituting the answer to (6a) into the answer to part (6b), write e as a convex linear combi nation of a, b, and c. (d) (d) Draw and label a, b, č, d, and e on the same grid. (e)) Draw the set of convex linear combinations of a, b, and c. Justify your answer. (e (a) +hd. (b) e= 8 Describe t (c) tion. (7 (g들 + D든)루 + 2든 =D2 + (d) e The set is the filled-in triangle with ver- tices given by a, b, and č. To see this, notice that the set of convex linear combi- nations of a, b, and c is the set of convex linear comhinations of and 9 Determi an tC
This is exactly the line given in vector form by vex the and t(a- b)b. ang -H l is the vertical line 2 Since a b 7 Let containing b (and a). following subse (d) Anl is the set (a All non-n faã +Bb a, p0 and a +B = 1} Ў. (b) All non-n This is the set of convex linear combina- tions of a and b. (c)) All conve (e)Anl is the line segment with endpoints a and b. (d) All conve (e) All conv The goal of and c 2 6 Let a - 1 - (a) T this question-is to give and justify a drawing of the set of convex linear combinations of a, b, and c. This requires an understanding of the previous question t -} (a)) Let Write as a convex linear combi- (b) nation of a and b. (b) Let ě = Write e as a convex linear combi- (c) nation of c and d. Substituting the answer to (6a) into the answer to part (6b), write e as a convex linear combi nation of a, b, and c. (d) (d) Draw and label a, b, č, d, and e on the same grid. (e)) Draw the set of convex linear combinations of a, b, and c. Justify your answer. (e (a) +hd. (b) e= 8 Describe t (c) tion. (7 (g들 + D든)루 + 2든 =D2 + (d) e The set is the filled-in triangle with ver- tices given by a, b, and č. To see this, notice that the set of convex linear combi- nations of a, b, and c is the set of convex linear comhinations of and 9 Determi an tC
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 18EQ
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