Let H= -{] : 8x² + 6y² 51}., 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. H is not a subspace of R² because the two vectors (Use a comma to separate vectors as needed.) 1 √8 0 0 1 √6 1 H is not a subspace of R² because the scalar 2 and the vector √8 0 show that H is not closed under addition. show that H is not closed under addition.
Let H= -{] : 8x² + 6y² 51}., 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. H is not a subspace of R² because the two vectors (Use a comma to separate vectors as needed.) 1 √8 0 0 1 √6 1 H is not a subspace of R² because the scalar 2 and the vector √8 0 show that H is not closed under addition. show that H is not closed under addition.
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=
{]
: 8x² + 6y² ≤ 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.
H is not a subspace of R² because the two vectors
(Use a comma to separate vectors as needed.)
col →
0
√8 1
0
√6
H is not a subspace of R² because the scalar 2 and the vector
1
√8
0
show that H is not closed under addition.
show that His not closed under addition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc7deb2c-0862-415e-88b2-023e0d274874%2Fbb907067-56ae-4f3e-ac35-5278d40345c2%2F6ebvrcs_processed.png&w=3840&q=75)
Transcribed Image Text:Let H=
{]
: 8x² + 6y² ≤ 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.
H is not a subspace of R² because the two vectors
(Use a comma to separate vectors as needed.)
col →
0
√8 1
0
√6
H is not a subspace of R² because the scalar 2 and the vector
1
√8
0
show that H is not closed under addition.
show that His not closed under addition.
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