1. Consider R3 with the usual addition of vectors, but with scalar multiplication defined by the attached image. Show that R3 togather with the operations addition and scalar multiplication is not vector space. 2. Let u= (attached image) and v= (attached image) be two vectors in R3. Consider the subset W = {au + bv : a, b is inside R}, of R3. Show that W is a subspace of R3. 1. Consider R³ with the usual addition + of vectors, but with scalar multiplication O definedbyko yky| 2kz]y ER³.%3DShow that R³ together with the operations + and © is not vector space.12. Let u =and v =3be two vectors in R³. Consider the subsetW = {au+bv : a, b e R},of R³. Show that W is a subspace of R³.

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Answered: 1. Consider R³ with the usual 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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1. Consider R³ with the usual addition of vectors, but with scalar multiplication defined by the attached image. Show that R³ togather with the operations addition and scalar multiplication is not vector space.

2. Let u= (attached image) and v= (attached image) be two vectors in R³. Consider the subset W = {au + bv : a, b is inside R},

of R³. Show that W is a subspace of R³.

1. Consider R³ with the usual addition + of vectors, but with scalar multiplication O defined
by
ko y
ky
| 2kz]
y ER³.
%3D
Show that R³ together with the operations + and © is not vector space.
1
2. Let u =
and v =
3
be two vectors in R³. Consider the subset
W = {au+bv : a, b e R},
of R³. Show that W is a subspace of R³.

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