. Let T : R2 → R² be defined by T((x,y)) = (2x – 3y, x + y), and let E = S = {(1,2), (2,3)}, bases for R?. {(1,0), (0, 1)} and (a) Find the matrix [T]E of T relative to E and the matrix [T]s of T relative to S. (b) Find P, the change of basis matrix from E to S. (c) Write an equation relating [T]E, [T]s, and P, and then verify that the equation is true by calculation.

. Let T : R2 → R² be defined by T((x,y)) = (2x – 3y, x + y), and let E = S = {(1,2), (2,3)}, bases for R?. {(1,0), (0, 1)} and (a) Find the matrix [T]E of T relative to E and the matrix [T]s of T relative to S. (b) Find P, the change of basis matrix from E to S. (c) Write an equation relating [T]E, [T]s, and P, and then verify that the equation is true by calculation.

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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