* Let X be the vector space of continuous real valued functions in [-1, 1]. Define (·, ·) : X×X → R as (x, y) = | x(1) y(1) dt. (a) Show that (-, ·) is a inner product. (b) Let Y c X be the set of even continuous real valued functions in [-1, 1]. That is, y € Y y(1) = y(-1) Vt e [-1,1]. Let Zc X be the set of odd continuous real valued functions in [-1,1]. That is, ze Z z(t) = -z(-1) VtE [-1,1]. Show that Y IZ.
* Let X be the vector space of continuous real valued functions in [-1, 1]. Define (·, ·) : X×X → R as (x, y) = | x(1) y(1) dt. (a) Show that (-, ·) is a inner product. (b) Let Y c X be the set of even continuous real valued functions in [-1, 1]. That is, y € Y y(1) = y(-1) Vt e [-1,1]. Let Zc X be the set of odd continuous real valued functions in [-1,1]. That is, ze Z z(t) = -z(-1) VtE [-1,1]. Show that Y IZ.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![3.* Let X be the vector space of continuous real valued functions in [-1, 1]. Define (·, ·) : X×X → R
as
(x, y)
= | x(1) y(1) dt.
(a) Show that (', ·) is a inner product.
(b) Let Y c X be the set of even continuous real valued functions in [-1, 1]. That is,
y € Y
y(t) = y(-1) Vt e [-1, 1].
Let Zc X be the set of odd continuous real valued functions in [-1, 1]. That is,
z E Z
z(t) = -z(-1) VtE [-1,1].
Show that Y IZ.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2731f2f8-549b-4c95-b876-fd63e857b145%2F77fd8a37-ff4e-459c-832d-3c7b61301241%2F8wim97_processed.png&w=3840&q=75)
Transcribed Image Text:3.* Let X be the vector space of continuous real valued functions in [-1, 1]. Define (·, ·) : X×X → R
as
(x, y)
= | x(1) y(1) dt.
(a) Show that (', ·) is a inner product.
(b) Let Y c X be the set of even continuous real valued functions in [-1, 1]. That is,
y € Y
y(t) = y(-1) Vt e [-1, 1].
Let Zc X be the set of odd continuous real valued functions in [-1, 1]. That is,
z E Z
z(t) = -z(-1) VtE [-1,1].
Show that Y IZ.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
