Let W be the union of the second and fourth quadrants in the xy-plane. That is, let W = parts a and b below. a. If u is in W and c is any scalar, is cu in W? Why? O A. X H-[x] If u = O B. X **-[x]- If u = X [] in W, then the vector cu = c X HR-[*]ish If u = X [] in W, then the vector cu = c is in W, then the vector cu = c X CX су CX cy -{[*] : Y=0} . CX is in W because cxy ≤0 since xy ≤ 0. Complete is not in W because cxy ≥ 0 in some cases. is in W because (cx) (cy) = c²(xy) ≤ 0 since xy ≤ 0. b. Find specific vectors u and v in W such that u + v is not in W. This is enough to show that W is not a vector space. Two vectors in W, u and v, for which u + v is not in W are (Use a comma to separate answers as needed.)
Let W be the union of the second and fourth quadrants in the xy-plane. That is, let W = parts a and b below. a. If u is in W and c is any scalar, is cu in W? Why? O A. X H-[x] If u = O B. X **-[x]- If u = X [] in W, then the vector cu = c X HR-[*]ish If u = X [] in W, then the vector cu = c is in W, then the vector cu = c X CX су CX cy -{[*] : Y=0} . CX is in W because cxy ≤0 since xy ≤ 0. Complete is not in W because cxy ≥ 0 in some cases. is in W because (cx) (cy) = c²(xy) ≤ 0 since xy ≤ 0. b. Find specific vectors u and v in W such that u + v is not in W. This is enough to show that W is not a vector space. Two vectors in W, u and v, for which u + v is not in W are (Use a comma to separate answers as needed.)
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
![Let W be the union of the second and fourth quadrants in the xy-plane. That is, let W =
parts a and b below.
a. If u is in W and c is any scalar, is cu in W? Why?
O A.
X
H-[x]
If u =
O B.
X
**-[x]-
If u =
X
[]
in W, then the vector cu = c
X
HR-[*]ish
If u =
X
[]
in W, then the vector cu = c
is in W, then the vector cu = c
X
CX
су
CX
cy
-{[*] : Y=0} .
CX
is in W because cxy ≤0 since xy ≤ 0.
Complete
is not in W because cxy ≥ 0 in some cases.
is in W because (cx) (cy) = c²(xy) ≤ 0 since xy ≤ 0.
b. Find specific vectors u and v in W such that u + v is not in W. This is enough to show that W is not a vector space.
Two vectors in W, u and v, for which u + v is not in W are
(Use a comma to separate answers as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F602f91a2-1aa7-412b-b03a-779222d25d63%2F02ffacce-b187-4c5a-b3f0-7a0e8cdd60d1%2Fg5a3ijv_processed.png&w=3840&q=75)
Transcribed Image Text:Let W be the union of the second and fourth quadrants in the xy-plane. That is, let W =
parts a and b below.
a. If u is in W and c is any scalar, is cu in W? Why?
O A.
X
H-[x]
If u =
O B.
X
**-[x]-
If u =
X
[]
in W, then the vector cu = c
X
HR-[*]ish
If u =
X
[]
in W, then the vector cu = c
is in W, then the vector cu = c
X
CX
су
CX
cy
-{[*] : Y=0} .
CX
is in W because cxy ≤0 since xy ≤ 0.
Complete
is not in W because cxy ≥ 0 in some cases.
is in W because (cx) (cy) = c²(xy) ≤ 0 since xy ≤ 0.
b. Find specific vectors u and v in W such that u + v is not in W. This is enough to show that W is not a vector space.
Two vectors in W, u and v, for which u + v is not in W are
(Use a comma to separate answers as needed.)
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