Let B={b,,..., b,} be a basis for a vector space V. You will be proving the following by filling in the blanks: If the set of coordinate vectors u,la: u, a is linearly dependent in R", then the subset u,} is linearly dependent in V. You need only write the word for each blank on our quiz, but be organized so I can grade your work. (a) If the set of vectors {u,a: [u,]a} is linearly dependent in (b) then there exist scalars c,- (where at least one c; is non-zero), (c) such that = 0 the zero vector in R" (d) By the of the coordinate mapping: „[u,] =[c«]la+ +[c,u,]a=[qu, + +c, +c, ...+ pp (e) (Note: c,u, is a vector in (f) Because 0, R" = [0, ]a' we can see that from above and part (c) that we have [gu, + ..+c,u,] =[0, ]g• Initial if you agree
Let B={b,,..., b,} be a basis for a vector space V. You will be proving the following by filling in the blanks: If the set of coordinate vectors u,la: u, a is linearly dependent in R", then the subset u,} is linearly dependent in V. You need only write the word for each blank on our quiz, but be organized so I can grade your work. (a) If the set of vectors {u,a: [u,]a} is linearly dependent in (b) then there exist scalars c,- (where at least one c; is non-zero), (c) such that = 0 the zero vector in R" (d) By the of the coordinate mapping: „[u,] =[c«]la+ +[c,u,]a=[qu, + +c, +c, ...+ pp (e) (Note: c,u, is a vector in (f) Because 0, R" = [0, ]a' we can see that from above and part (c) that we have [gu, + ..+c,u,] =[0, ]g• Initial if you agree
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(g) Because the coordinate mapping is
[qu, + ..+c,u, ] =[0,]a implies qu, + .+c,u, = 0, .
...+ C.
v ]B
(h) Therefore, the set of vectors
is](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb055c63f-89a3-4c28-8011-cd1d10eeedf8%2Fd66999c2-f368-49ab-9141-f6b078fdf2e0%2Ftfts4up_processed.png&w=3840&q=75)
Transcribed Image Text:(g) Because the coordinate mapping is
[qu, + ..+c,u, ] =[0,]a implies qu, + .+c,u, = 0, .
...+ C.
v ]B
(h) Therefore, the set of vectors
is
![Let B={b,,...,b,} be a basis for a vector space V. You will be proving the
following by filling in the blanks:
If the set of coordinate vectors {[u,la u, a is linearly dependent in R", then the subset
{u,u,} is linearly dependent in V.
You need only write the word for each blank on our quiz, but be organized so I can grade
your work.
(a) If the set of vectors {u,a
·[u,] is linearly dependent in
(b) then there exist scalars c,,
(where at least one c, is non-zero),
(c) such that
= 0
the zero vector in R" .
(d) By the
of the coordinate mapping:
G[u,]a+
+Cpup
си.
...+C
u
+
+
+ -..
(e) (Note: c,u, is a vector in
(f) Весause 0.
R"
=|0, la, we can see that from above and part (c) that we have
[qu, +.+c,u,]=[0, la: Initial if you agree
+c̟u,
pp ]B](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb055c63f-89a3-4c28-8011-cd1d10eeedf8%2Fd66999c2-f368-49ab-9141-f6b078fdf2e0%2Fh3766v_processed.png&w=3840&q=75)
Transcribed Image Text:Let B={b,,...,b,} be a basis for a vector space V. You will be proving the
following by filling in the blanks:
If the set of coordinate vectors {[u,la u, a is linearly dependent in R", then the subset
{u,u,} is linearly dependent in V.
You need only write the word for each blank on our quiz, but be organized so I can grade
your work.
(a) If the set of vectors {u,a
·[u,] is linearly dependent in
(b) then there exist scalars c,,
(where at least one c, is non-zero),
(c) such that
= 0
the zero vector in R" .
(d) By the
of the coordinate mapping:
G[u,]a+
+Cpup
си.
...+C
u
+
+
+ -..
(e) (Note: c,u, is a vector in
(f) Весause 0.
R"
=|0, la, we can see that from above and part (c) that we have
[qu, +.+c,u,]=[0, la: Initial if you agree
+c̟u,
pp ]B
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