Consider the following linear transformation and basis. Find the standard matrix A for the linear transformation. A = P = T: R² R², T(x, y) = (x - y, 3y-x), B' = {(1, -2), (0,3)} Find the transition matrix P from B' to the standard basis B and then find its inverse. 7 ↓t A' = ↓ 1 ↓ 1 Find the matrix A' for T relative to the basis B'. 35 ↓1
Consider the following linear transformation and basis. Find the standard matrix A for the linear transformation. A = P = T: R² R², T(x, y) = (x - y, 3y-x), B' = {(1, -2), (0,3)} Find the transition matrix P from B' to the standard basis B and then find its inverse. 7 ↓t A' = ↓ 1 ↓ 1 Find the matrix A' for T relative to the basis B'. 35 ↓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 17CM
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![Consider the following linear transformation and basis.
Find the standard matrix A for the linear transformation.
A =
P =
T: R² R², T(x, y) = (x - y, 3y-x), B' = {(1, -2), (0,3)}
Find the transition matrix P from B' to the standard basis B and then find its inverse.
7
↓t
A' =
↓ 1
↓ 1
Find the matrix A' for T relative to the basis B'.
35](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b9fb947-7d87-49f8-9e34-2adf636f2bfd%2F65cc4ca4-bde8-4779-a921-775559b14ae4%2Fjwtfx2f_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following linear transformation and basis.
Find the standard matrix A for the linear transformation.
A =
P =
T: R² R², T(x, y) = (x - y, 3y-x), B' = {(1, -2), (0,3)}
Find the transition matrix P from B' to the standard basis B and then find its inverse.
7
↓t
A' =
↓ 1
↓ 1
Find the matrix A' for T relative to the basis B'.
35
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