Consider the function T : R³ → R³ defined by T(x, y, 2) = (3x, x – y, 2x + y+ 2). (i) Prove that T is a linear transformation. (ii) Find the representing matrix of T relative to the basis 3 = {a1 (1, 1, 1)} of R³. (1,0, 0), a2 (1, 1,0), a3

Consider the function T : R³ → R³ defined by T(x, y, 2) = (3x, x – y, 2x + y+ 2). (i) Prove that T is a linear transformation. (ii) Find the representing matrix of T relative to the basis 3 = {a1 (1, 1, 1)} of R³. (1,0, 0), a2 (1, 1,0), a3

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 function T : R³ → R³ defined by T(x, y, 2) = (3x, x – y, 2x + y+ 2).
(i) Prove that T is a linear transformation.
(ii) Find the representing matrix of T relative to the basis 3 = {a1
(1, 1, 1)} of R³.
(1,0, 0), a2
(1, 1,0), a3

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