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.

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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Question

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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Follow-up Question

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

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