Let V be the vector space C([-1,1]) of continuous functions on interval [-1,1] equipped with the scalar product (f\g) = f f(t)\g(t)dt. a) Find the length of f(t) = e ¹0t and g(t) = e-1⁰t in V b) Find the angle between fand g from (a) c) Is this angle similar to any angle you know?
Let V be the vector space C([-1,1]) of continuous functions on interval [-1,1] equipped with the scalar product (f\g) = f f(t)\g(t)dt. a) Find the length of f(t) = e ¹0t and g(t) = e-1⁰t in V b) Find the angle between fand g from (a) c) Is this angle similar to any angle you know?
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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![Let V be the vector space C([-1,1]) of continuous functions on interval [−1,1] equipped
with the scalar product
(f\g) = f, f(t)\g(t)dt.
a) Find the length of f(t) 10t and g(t) = e
-10t
= e
b) Find the angle between fand g from (a)
c) Is this angle similar to any angle you know?
in V](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90908fc3-5ffe-4920-b171-443d19ac1d81%2F241b23ed-d7c4-4070-9dd3-88da978e5664%2Fk7eil5g_processed.png&w=3840&q=75)
Transcribed Image Text:Let V be the vector space C([-1,1]) of continuous functions on interval [−1,1] equipped
with the scalar product
(f\g) = f, f(t)\g(t)dt.
a) Find the length of f(t) 10t and g(t) = e
-10t
= e
b) Find the angle between fand g from (a)
c) Is this angle similar to any angle you know?
in V
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