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

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

  2. Find the matrix representation B of T in the basis f = (f1, f2) where f1 = (1,1) and f2 = (2,1).

  3. Find the change of basis matrix P from e to f

  4. Find the change of basis matrix Q from f to e

  5. Find a relation between A, B, P and Q, and prove that your

    relation holds by computing the matrix products.

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