IV. Let L be the operator given by L[y] = y"" – 2y" + 2u" i. Consider L as a linear operator T : P3 → P3. Find [T], where a is the standard basis of P3 ii. Determine the kernel of L from part i. iii. Now, consider L as a transformation L: Co (R) → C (R). Find the kernel of L.

IV. Let L be the operator given by L[y] = y"" – 2y" + 2u" i. Consider L as a linear operator T : P3 → P3. Find [T], where a is the standard basis of P3 ii. Determine the kernel of L from part i. iii. Now, consider L as a transformation L: Co (R) → C (R). Find the kernel of L.

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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Question

IV. Let L be the operator given by L[y] = y"" – 2y" + 2u"
i. Consider L as a linear operator T : P3 → P3. Find [T], where a is the standard
basis of P3
ii. Determine the kernel of L from part i.
iii. Now, consider L as a transformation L: Co (R) → C (R). Find the kernel of L.

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