Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
Related questions
Question
![a
Q.8. Let the set H =-
: a² +b? >1}. Is set H a vector space? Justify your answer.
Q.9. Let the set H =
:ab<1
(a) Is set H a vector space? Justify your answer.
(b) Is the set H close with respect to scalar multiplication? Justify your answer
q
Q.10. Determine if the set H of all matrices of the form
is a subspace of M2. Here, p, q and
2x2
r
r represent arbitrary real numbers.
Q.11. Let H be the set of all vectors of the form shown below. Is H a subspace of R*? Justify your
answer for each case. Here, p,q,r and s represent arbitrary real numbers.
p+q-s
[2p-s|
p-r
(a)
2р+39
р-2
(b)
p+3q
r+3q
|1 2 3 4
5
[1
Q.12. Let A =0 1 2 3 -1
u =
and v =|0
2 0 12 -2
(a) Determine if u e NulA. Could u e ColA? Justify.
(b) Determine if ve CollA. Could v e NulA? Justify.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F323d4d09-9993-48e4-b43f-5136d4a27736%2Fc49e0fc1-ade8-4e42-b38f-9d6b71a18c0d%2Fi0omfhf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a
Q.8. Let the set H =-
: a² +b? >1}. Is set H a vector space? Justify your answer.
Q.9. Let the set H =
:ab<1
(a) Is set H a vector space? Justify your answer.
(b) Is the set H close with respect to scalar multiplication? Justify your answer
q
Q.10. Determine if the set H of all matrices of the form
is a subspace of M2. Here, p, q and
2x2
r
r represent arbitrary real numbers.
Q.11. Let H be the set of all vectors of the form shown below. Is H a subspace of R*? Justify your
answer for each case. Here, p,q,r and s represent arbitrary real numbers.
p+q-s
[2p-s|
p-r
(a)
2р+39
р-2
(b)
p+3q
r+3q
|1 2 3 4
5
[1
Q.12. Let A =0 1 2 3 -1
u =
and v =|0
2 0 12 -2
(a) Determine if u e NulA. Could u e ColA? Justify.
(b) Determine if ve CollA. Could v e NulA? Justify.
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