-{] Let W be the union of the first and third quadrants in the xy-plane. That is, let W = a. If u is in W and c is any scalar, is cu in W? Why? O A. O B. O C. X -[] y If u = If u = If u = X X is in W, then the vector cu = C is in W, then the vector cu = c CX H] су is in W, then the vector cu = c X CX су xy ≥0. Complete parts a and b below. is not in W because cxy ≤0 in some cases. CX [][] су is in W because cxy ≥0 since xy 20. 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 first and third quadrants in the xy-plane. That is, let W = a. If u is in W and c is any scalar, is cu in W? Why? O A. O B. O C. X -[] y If u = If u = If u = X X is in W, then the vector cu = C is in W, then the vector cu = c CX H] су is in W, then the vector cu = c X CX су xy ≥0. Complete parts a and b below. is not in W because cxy ≤0 in some cases. CX [][] су is in W because cxy ≥0 since xy 20. 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 first and third quadrants in the xy-plane. That is, let W =
a. If u is in W and c is any scalar, is cu in W? Why?
O A.
O B.
O C.
X
-[]
y
If u =
If u =
If u =
X
X
is in W, then the vector cu = C
is in W, then the vector cu = c
CX
H]
су
is in W, then the vector cu = c
X
CX
су
xy ≥0. Complete parts a and b below.
is not in W because cxy ≤0 in some cases.
CX
[][]
су
is in W because cxy ≥0 since xy 20.
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%2Ff31d497b-3620-469b-803c-c1a53df0f79e%2F1f6250cc-5047-48c8-ae6b-e1d155c2b387%2F5nvajs4_processed.png&w=3840&q=75)
Transcribed Image Text:-{]
Let W be the union of the first and third quadrants in the xy-plane. That is, let W =
a. If u is in W and c is any scalar, is cu in W? Why?
O A.
O B.
O C.
X
-[]
y
If u =
If u =
If u =
X
X
is in W, then the vector cu = C
is in W, then the vector cu = c
CX
H]
су
is in W, then the vector cu = c
X
CX
су
xy ≥0. Complete parts a and b below.
is not in W because cxy ≤0 in some cases.
CX
[][]
су
is in W because cxy ≥0 since xy 20.
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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