Let T: P₂ → R² be the linear transformation. Given that M = (1,x+x²,2-3x2) and N = {(₁).(2)} are bases for P2 and R² respectively. a) Let T(a + bx + cx²) = (+b). i. Find the standard matrix, A for T such that T(v) = Av for v € P₂. ii. Find [T]NM, the matrix of T with respect to the bases M and N. b) If [v]M2, find T(v) using matrix [T]NM obtained in (a). -11-₁
Let T: P₂ → R² be the linear transformation. Given that M = (1,x+x²,2-3x2) and N = {(₁).(2)} are bases for P2 and R² respectively. a) Let T(a + bx + cx²) = (+b). i. Find the standard matrix, A for T such that T(v) = Av for v € P₂. ii. Find [T]NM, the matrix of T with respect to the bases M and N. b) If [v]M2, find T(v) using matrix [T]NM obtained in (a). -11-₁
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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![Let T: P₂ → R² be the linear transformation. Given that M = {1,x+x²,2-3x²] and N =
{(₁). (2)} are bases for P2 and R² respectively.
a) Let T(a + bx + cx²) = (+b).
i.
Find the standard matrix, A for T such that T(v) = Av for v € P₂.
Find [T]NM, the matrix of T with respect to the bases M and N.
b)
If [v]M2, find T(v) using matrix [T]NM obtained in (a).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ad01f60-4219-492f-ba73-b52c85c2a06b%2Fb979e639-259b-41c7-b824-da5c22bd9c1c%2Fpiofh8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let T: P₂ → R² be the linear transformation. Given that M = {1,x+x²,2-3x²] and N =
{(₁). (2)} are bases for P2 and R² respectively.
a) Let T(a + bx + cx²) = (+b).
i.
Find the standard matrix, A for T such that T(v) = Av for v € P₂.
Find [T]NM, the matrix of T with respect to the bases M and N.
b)
If [v]M2, find T(v) using matrix [T]NM obtained in (a).
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