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
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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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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