1. Consider the linear transformation T : R3 R2, defined on the standard basis aof R by T(1,0, 0) = (-1,3), T(0, 1,0) = (4, –3), T(0,0, 1) = (5,-2). Finda) The matrix [T]a•b) T(r, y, z) for any vector (x, y, z), and particularly T(2,6, 9).c) The kernel of T, Ker(T).

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Answered: 1. Consider the linear transformation…

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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1. Consider the linear transformation T: R3 R2, defined on the standard basis a of R° by T(1,0, 0) = (-1, 3), T(0, 1,0) = (4, -3), T(0,0, 1) = (5,-2). Find a) The matrix [T]a• b) T(r, y, z) for any vector (r, y, z), and particularly T(2, 6,9). c) The kernel of T, Ker(T).