Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
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)?
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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)?
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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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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Step 1: Define one to one and onto
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Step 2: Proving T is one to one but not onto
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Step 3: Attempt to define the inverse transformation
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