[] : 2x² +8y² ≤1 which represents the set of points on and inside an ellipse in the xy-plane. Find two specific examples-two vectors, and a vector and a scalar-to show that H is not a subspace of R². Let H= H is not a subspace of R2 because the two vectors √2 0 (Use a comma to separate vectors as needed.) H is not a subspace of R2 because the scalar 2 and the vector 0 1 √8 show that H is not closed under addition. show that H is not closed under scalar multiplication.
[] : 2x² +8y² ≤1 which represents the set of points on and inside an ellipse in the xy-plane. Find two specific examples-two vectors, and a vector and a scalar-to show that H is not a subspace of R². Let H= H is not a subspace of R2 because the two vectors √2 0 (Use a comma to separate vectors as needed.) H is not a subspace of R2 because the scalar 2 and the vector 0 1 √8 show that H is not closed under addition. show that H is not closed under scalar multiplication.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let H=
{ ;]*•*^^}
{]
: 2x² + 8y² ≤1
a subspace of R².
which represents the set of points on and inside an ellipse in the xy-plane. Find two specific examples-two vectors, and a vector and a scalar-to show that H is not
H is not a subspace of R2 because the two vectors
1
√√2
0
(Use a comma to separate vectors as needed.)
H is not a subspace of R2 because the scalar 2 and the vector
√8
show that H is not closed under addition.
show that H is not closed under scalar multiplication.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0058694e-01c1-4ca5-8fce-b9137a5384c6%2F9d44321d-8349-4754-8390-6fdd9bd4f85f%2F36mnox9_processed.png&w=3840&q=75)
Transcribed Image Text:Let H=
{ ;]*•*^^}
{]
: 2x² + 8y² ≤1
a subspace of R².
which represents the set of points on and inside an ellipse in the xy-plane. Find two specific examples-two vectors, and a vector and a scalar-to show that H is not
H is not a subspace of R2 because the two vectors
1
√√2
0
(Use a comma to separate vectors as needed.)
H is not a subspace of R2 because the scalar 2 and the vector
√8
show that H is not closed under addition.
show that H is not closed under scalar multiplication.
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