5. C.Let : R₂[x] R³ be a linear transformation such that0(6)l(x) ==--------andl(x²) =(a) Find a formula for l(a + bx + cx²).(b) Show that is a vector space isomorphism and find a formula for l-¹.

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Answered: C. Let l: R₂[x] → R³ be a linear…

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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C. Let l: R₂[x] → R³ be a linear transformation such that (6) l(1) = l(x) = = 1 and l(x²) = (a) Find a formula for l(a + bx + cx²). (b) Show that is a vector space isomorphism and find a formula for l-¹.