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This is exactly the line given in vectorform byvextheandt(a- b)b.ang-Hl is the vertical line2Since a b7 Letcontaining b (and a).following subse(d) Anl is the set(a All non-nfaã +Bb a, p0 and a +B = 1}Ў.(b) All non-nThis is the set of convex linear combina-tions of a and b.(c)) All conve(e)Anl is the line segment with endpointsa and b.(d) All conve(e) All convThe goal ofand c26 Let a-1-(a) Tthis question-is to give and justify a drawing of theset of convex linear combinations of a, b, and c. Thisrequires an understanding of the previous questiont-}(a)) LetWriteas 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 answerto part (6b), write e as a convex linear combination of a, b, and c.(d)(d) Draw and label a, b, č, d, and e on the samegrid.(e)) Draw the set of convex linear combinations ofa, 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 convexlinear comhinations of and9 DetermiantC

Question

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
help_outline

Image Transcriptionclose

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

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Step 1

The problem concerns convex linear combinations of vectors

Step 2

Similarly, if three vectors (non collinear) u, v and w are given, then the set of convex linear combinations consists of pu+qv+rw, with p,q,r lying between 0 a...

Let uv be vectors.The set of
convex linear combinations
{pu(p)v 0<p<l}
(The line segment joining the
end point s of the two vectors)
help_outline

Image Transcriptionclose

Let uv be vectors.The set of convex linear combinations {pu(p)v 0<p<l} (The line segment joining the end point s of the two vectors)

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