5.3) Let : R₂[x] → R³ be a linear transformation such that((1) ==l(x):=0andl(x²) ==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.

Answered: Image /qna-images/answer/e4f340b9-b80a-477a-9fe2-9db8347ea234.jpg

5. 3) Let : R₂[x] →→ R³ be a linear transformation such that (6) (a) Find a formula for l(a + bx + cx²). (b) Show that is a vector space isomorphism and find a formula for l-¹. (1) = = l(x): = 0 and l(x²) = = 1

5. 3) Let : R₂[x] →→ R³ be a linear transformation such that (6) (a) Find a formula for l(a + bx + cx²). (b) Show that is a vector space isomorphism and find a formula for l-¹. (1) = = l(x): = 0 and l(x²) = = 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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Question

5.
3) Let : R₂[x] → R³ be a linear transformation such that
(
(1) =
=
l(x):
=
0
and
l(x²) =
=
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.

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