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- 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
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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- 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.)
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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