X Let W be the union of the first and third quadrants in the xy-plane. That is, let W = () and b below. a. If uis in W and c is any scalar, is cu in W? Why? X -[:] O A. O B. O C. If u = If u = If u = X [H] is in W, then the vector cu = c X CX =[H] cy is in W, then the vector cu = c > is in W, then the vector cu = c is in W because cxy ≥0 since xy ≥0. :xy 205. Complete parts a : xyz0}. X CX =[][] y cy is in W because (cx) (cy) = c²2(xy) 20 since xy 20. is not in W because cxy ≤0 in some cases.
X Let W be the union of the first and third quadrants in the xy-plane. That is, let W = () and b below. a. If uis in W and c is any scalar, is cu in W? Why? X -[:] O A. O B. O C. If u = If u = If u = X [H] is in W, then the vector cu = c X CX =[H] cy is in W, then the vector cu = c > is in W, then the vector cu = c is in W because cxy ≥0 since xy ≥0. :xy 205. Complete parts a : xyz0}. X CX =[][] y cy is in W because (cx) (cy) = c²2(xy) 20 since xy 20. is not in W because cxy ≤0 in some cases.
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
Transcribed Image Text: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.)
![X
Let W be the union of the first and third quadrants in the xy-plane. That is, let W =
()
and b below.
a. If uis in W and c is any scalar, is cu in W? Why?
X
-[:]
O A.
O B.
O C.
If u =
If u =
If u =
X
[H]
is in W, then the vector cu = c
X
CX
=[H]
cy
is in W, then the vector cu = c
>
is in W, then the vector cu = c
is in W because cxy 20 since xy 20.
:xy 205. Complete parts a
: xyz0}.
X
CX
=[][]
y
cy
is in W because (cx) (cy) = c²2(xy) ≥ 0 since xyz0.
is not in W because cxy ≤0 in some cases.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb73e221-fc24-4f22-8ff5-c1a81fef495f%2Fc5157b7f-c158-4e3b-b498-b8f1ea23a268%2Fl0sjmib_processed.png&w=3840&q=75)
Transcribed Image Text:X
Let W be the union of the first and third quadrants in the xy-plane. That is, let W =
()
and b below.
a. If uis in W and c is any scalar, is cu in W? Why?
X
-[:]
O A.
O B.
O C.
If u =
If u =
If u =
X
[H]
is in W, then the vector cu = c
X
CX
=[H]
cy
is in W, then the vector cu = c
>
is in W, then the vector cu = c
is in W because cxy 20 since xy 20.
:xy 205. Complete parts a
: xyz0}.
X
CX
=[][]
y
cy
is in W because (cx) (cy) = c²2(xy) ≥ 0 since xyz0.
is not in W because cxy ≤0 in some cases.
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