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.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 3CM: Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions...
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5. C.
Let : R₂[x] R³ be a linear transformation such that
0
(6)
l(x) =
=
--------
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.
Transcribed Image Text:5. C. Let : R₂[x] R³ be a linear transformation such that 0 (6) l(x) = = -------- 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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