Let T: P Pa be the linear transformation defined by T(at3 + bt2 + ct +d) = (a – b)t3 + (c- d)t. Then, justify your answers:4.1)%3D(i) Is T invertible?(ii) Is t3 - t2 + t - 1 in ker T ?(iii) Is 3t3 + t in range T ?(iv) Find a basis of ker T.(v) Find a basis of range T.

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Answered: Let T: P3 Pa be the linear…

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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Let T: P3 Pa be the linear transformation defined by T(at3 + bt2 + ct + d) = (a - b)t3+ (c- d)t. Then, justify your answers: %3D (i) Is T invertible? (ii) Is t3 – t2 +t- 1 in ker T ? (iii) Is 3t3 + t in range T ? (iv) Find a basis of ker T. (v) Find a basis of range T. 4.