Problem 5 Let T : P2 → P2 be the linear transformation defined by T(p(x)) = p(x + 2). Find the matrir representation [T]c,g of T with respect to the ordered bases B = {1,x +2, (x +2)²} and C = {1,x, x²}. Check that the representation is correct by computing T(a + bx + cx?) both directly and by using the matrix representation.
Problem 5 Let T : P2 → P2 be the linear transformation defined by T(p(x)) = p(x + 2). Find the matrir representation [T]c,g of T with respect to the ordered bases B = {1,x +2, (x +2)²} and C = {1,x, x²}. Check that the representation is correct by computing T(a + bx + cx?) both directly and by using the matrix representation.
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 11CM
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The transformation is from the base B to the base C.
![Problem 5 Let T : P2 → P2 be the linear transformation defined by T(p(x)) = p(x+ 2).
Find the matrix representation [T]c,B of T with respect to the ordered bases
B = {1,x + 2, (x + 2)?}
and
C = {1, x, x²}.
Check that the representation is correct by computing T(a + bx + cx?) both directly and by
using the matrix representation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88e1e2e4-888b-4182-8c02-fd46dda7f6b1%2F29f90887-42c7-4195-9879-2b17165d14c1%2Fmrnrgvf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 5 Let T : P2 → P2 be the linear transformation defined by T(p(x)) = p(x+ 2).
Find the matrix representation [T]c,B of T with respect to the ordered bases
B = {1,x + 2, (x + 2)?}
and
C = {1, x, x²}.
Check that the representation is correct by computing T(a + bx + cx?) both directly and by
using the matrix representation.
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