- For a positive integer n, le Pn(r) = (x + 1)(r+2) (x + n). Show that the set of polynomials Pn (x) Pn(r) I+1'r+2 Pn(x) I+n] is linearly independent for any n. For example, the set for n = 3 is {(r + 2)(r + 3), (x + 1)(x + 3), (x + 1)(x + 2)}. (Hint: Set up a linear independence argument and try evaluating for r at certain values.)
- For a positive integer n, le Pn(r) = (x + 1)(r+2) (x + n). Show that the set of polynomials Pn (x) Pn(r) I+1'r+2 Pn(x) I+n] is linearly independent for any n. For example, the set for n = 3 is {(r + 2)(r + 3), (x + 1)(x + 3), (x + 1)(x + 2)}. (Hint: Set up a linear independence argument and try evaluating for r at certain values.)
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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i would like help with question 5
![- For a positive integer n, le Pn(r) = (x + 1)(r+2) (x + n). Show that the set of
polynomials
Pn (x) Pn(r)
I+1'r+2
Pn(x)
I+n]
is linearly independent for any n.
For example, the set for n = 3 is {(r + 2)(r + 3), (x + 1)(x + 3), (x + 1)(x + 2)}.
(Hint: Set up a linear independence argument and try evaluating for r at certain
values.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16587444-2baf-4a64-89bf-0dbc007ed50f%2Fc3324ab2-3892-48ee-b87b-41a296642dff%2Frok8cj4.jpeg&w=3840&q=75)
Transcribed Image Text:- For a positive integer n, le Pn(r) = (x + 1)(r+2) (x + n). Show that the set of
polynomials
Pn (x) Pn(r)
I+1'r+2
Pn(x)
I+n]
is linearly independent for any n.
For example, the set for n = 3 is {(r + 2)(r + 3), (x + 1)(x + 3), (x + 1)(x + 2)}.
(Hint: Set up a linear independence argument and try evaluating for r at certain
values.)
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