Let : R₂[x] → R³ be a linear transformation such that l(1) = 0 1 l(x) = 1 and l(x²) = 0 1 1 (a) Find a formula for l(a + bx + cx²). (b) Show that is a vector space isomorphism and find a formula for l-¹.
Let : R₂[x] → R³ be a linear transformation such that l(1) = 0 1 l(x) = 1 and l(x²) = 0 1 1 (a) Find a formula for l(a + bx + cx²). (b) Show that is a vector space isomorphism and find a formula for l-¹.
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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Help me answer a and b please
![Let l: R₂[x] → R³ be a linear transformation such that
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F850cccdb-7a8f-4495-9a49-b5538d79e182%2F0610b16a-c493-4cb9-bd97-8c737ba92f09%2Fyu8980s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let l: R₂[x] → R³ be a linear transformation such that
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.
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