Consider the linear transformation T ∶ R2 → R2 defined by T (x, y) = (x − y, 2x + y).Find the matrix representation A of T in the basis e = (e1,e2) where e1 = (1,4) and e2 = (2,7).Find the matrix representation B of T in the basis f = (f1, f2) where f1 = (1,1) and f2 = (2,1).Find the change of basis matrix P from e to fFind the change of basis matrix Q from f to eFind a relation between A, B, P and Q, and prove that yourrelation holds by computing the matrix products.

Write T(e1) as a linear combination of e1 and e2Write T(e2) as a linear combination of e1 and e2.…

Answered: Find the matrix representation A of T…

Find the matrix representation A of T in the basis e = (e1,e2) where e1 = (1,4) and e2 = (2,7). Find the matrix representation B of T in the basis f = (f1, f2) where f1 = (1,1) and f2 = (2,1).

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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Question

Consider the linear transformation T ∶ R2 → R2 defined by T (x, y) = (x − y, 2x + y).

Find the matrix representation A of T in the basis e = (e1,e2) where e1 = (1,4) and e2 = (2,7).
Find the matrix representation B of T in the basis f = (f1, f2) where f1 = (1,1) and f2 = (2,1).
Find the change of basis matrix P from e to f
Find the change of basis matrix Q from f to e
Find a relation between A, B, P and Q, and prove that your

relation holds by computing the matrix products.

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