5. a) Prove that T is one to one but not onto. b) Attempt to define T-¹: P4 → P3 as in for- mula (1) by setting T-¹(q) = p if and only if T(p) = q. What is T-¹(x)?
5. a) Prove that T is one to one but not onto. b) Attempt to define T-¹: P4 → P3 as in for- mula (1) by setting T-¹(q) = p if and only if T(p) = q. What is T-¹(x)?
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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Transcribed Image Text:5. a) Prove that T is one to one but not onto.
b) Attempt to define T-¹: P4 → P3 as in for-
mula (1) by setting T-¹ (q) = p if and only if
T(p) = q. What is T-¹(x)?
Transcribed Image Text:In Exercises 1–6, the linear transformations S, T, and
H are defined as follows:
S:P3 → P4 is defined by S(p) = p'(0).
T:P3 → P4 is defined by T (p) = (x + 2)p(x).
H:P4 → P3 is defined by H(p) = p'(x) + p(0).
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