Let W be the union of the second and fourth quadrants in the xy-plane. That is, let W = and b below. a. If u is in W and c is any scalar, is cu in W? Why? X -D If u = у A. B. If u = X y is in W, then the vector cu = c X **-** If u = y [3]- y is in W, then the vector cu = c CX X CX [][] y су is in W, then the vector cu = c су X {*]: xY=O). X CX [][] = y су is not in W because cxy 20 in some cases. Complete parts a is in W because (cx) (cy) = c²(xy) ≤0 since xy ≤0. is in W because cxy ≤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 = and b below. a. If u is in W and c is any scalar, is cu in W? Why? X -D If u = у A. B. If u = X y is in W, then the vector cu = c X **-** If u = y [3]- y is in W, then the vector cu = c CX X CX [][] y су is in W, then the vector cu = c су X {*]: xY=O). X CX [][] = y су is not in W because cxy 20 in some cases. Complete parts a is in W because (cx) (cy) = c²(xy) ≤0 since xy ≤0. is in W because cxy ≤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 =
and b below.
a. If u is in W and c is any scalar, is cu in W? Why?
A.
B.
If u =
If u =
If u =
X
y
X
y
X
y
is in W, then the vector cu = c
is in W, then the vector cu = c
is in W, then the vector cu = c
X
y
X
y
X
y
=
=
=
CX
cy
CX
CX
X
{] : xyso).
y
cy
is in W because (cx) (cy) = c²(xy) ≤0 since xy ≤0.
cy
Complete parts a
is not in W because cxy 20 in some cases.
is in W because cxy ≤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%2Fbea0901b-9b71-43dc-90d5-d9e10ed3de89%2F27a14306-c27b-412e-9c47-1181a96f2997%2Fmi2nvhp_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 =
and b below.
a. If u is in W and c is any scalar, is cu in W? Why?
A.
B.
If u =
If u =
If u =
X
y
X
y
X
y
is in W, then the vector cu = c
is in W, then the vector cu = c
is in W, then the vector cu = c
X
y
X
y
X
y
=
=
=
CX
cy
CX
CX
X
{] : xyso).
y
cy
is in W because (cx) (cy) = c²(xy) ≤0 since xy ≤0.
cy
Complete parts a
is not in W because cxy 20 in some cases.
is in W because cxy ≤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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