Let H= X { ;] 182² +47²=1}\x 5x² y 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.

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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X
{ ;] 182²+47²=1}\x
y
Let H=
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
under
(Use a comma to separate vectors as needed.)
show that H
closed
Transcribed Image Text:X { ;] 182²+47²=1}\x y Let H= 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 under (Use a comma to separate vectors as needed.) show that H closed
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1. 
2. is / is not
3. addition / scalar multiplication

X
{]
: 5x² + 4y² ≤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
1
addition.
(Use a comma to separate vectors as needed.)
H is not a subspace of R2 because the scalar 4 and the vector
NI →
2
show that H is not closed under
show that H
closed under
Transcribed Image Text:X {] : 5x² + 4y² ≤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 1 addition. (Use a comma to separate vectors as needed.) H is not a subspace of R2 because the scalar 4 and the vector NI → 2 show that H is not closed under show that H closed under
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