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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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This problem is from Linear Algebra. It's based on Module 2. The book is called Linear Algebra Math Workbook 282 by Jason Siefken

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

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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