2. Given: L : R² → R², L(x, y) = (x + 2y, 2x - y), ordered bases B = {(-1, 2), (2,0)}, B' = {(1,-1), (1, 2)} a. Find the matrix representation of L wrt B. b. Find the change of basis matrix: (i.) from B' to B; (ii.) from B to B' c. Determine the matrix rep. of L wrt B' using the matrices in (a) and (b).
2. Given: L : R² → R², L(x, y) = (x + 2y, 2x - y), ordered bases B = {(-1, 2), (2,0)}, B' = {(1,-1), (1, 2)} a. Find the matrix representation of L wrt B. b. Find the change of basis matrix: (i.) from B' to B; (ii.) from B to B' c. Determine the matrix rep. of L wrt B' using the matrices in (a) and (b).
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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![2. Given: L: R² → R², L(x, y) = (x + 2y, 2x - y), ordered bases B = {(-1,2), (2,0)}, B' =
{(1,-1), (1, 2)}
a. Find the matrix representation of L wrt B.
b. Find the change of basis matrix: (i.) from B' to B; (ii.) from B to B'
c. Determine the matrix rep. of L wrt B' using the matrices in (a) and (b).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F549c0f6b-4e44-4eda-abb4-7d896557ad6b%2F30d65760-3f78-40a3-9166-ce933d09911a%2F8zlg0dm_processed.png&w=3840&q=75)
Transcribed Image Text:2. Given: L: R² → R², L(x, y) = (x + 2y, 2x - y), ordered bases B = {(-1,2), (2,0)}, B' =
{(1,-1), (1, 2)}
a. Find the matrix representation of L wrt B.
b. Find the change of basis matrix: (i.) from B' to B; (ii.) from B to B'
c. Determine the matrix rep. of L wrt B' using the matrices in (a) and (b).
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