Please help me with this linear algebra review question. THIS IS NOT FOR POINTS OR A GRADE! 0(8)the yz-plane in three dimensional space (see picture below).1. Let H =XX:y and z are real numbers. In other words, H isxz-planeZA0yz-planeplane? (2 pts)(a) Does H contain the zero vector,0(b) Is H closed under vector addition? If not, find vectors u and v inH such that u + v is not in H. (2 pts)(c) Is H closed under scalar multiplication? If not, find a scalar (realnumber) c and a vector u in H such that cu is not in H. (2 pts)(d) Is H a subspace of R3? If yes, find a basis for H. (2 pts)

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Answered: 1. Let H = :y and z are real numbers In…

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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Please help me with this linear algebra review question. THIS IS NOT FOR POINTS OR A GRADE!

0
(8)
the yz-plane in three dimensional space (see picture below).
1. Let H =
XX
:y and z are real numbers. In other words, H is
xz-plane
ZA
0
yz-plane
plane
? (2 pts)
(a) Does H contain the zero vector,
0
(b) Is H closed under vector addition? If not, find vectors u and v in
H such that u + v is not in H. (2 pts)
(c) Is H closed under scalar multiplication? If not, find a scalar (real
number) c and a vector u in H such that cu is not in H. (2 pts)
(d) Is H a subspace of R3? If yes, find a basis for H. (2 pts)

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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