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2 3 4 1 4 3 2 3 4 1) 1 2 2. Let X = {1,2, 3, 4}. Consider the following elements of P(X): a = (; 2 3 4 (1 2 3 4 y = \1 3 4 2 a) How many elements are in the group P(X)? b) Calculate aß, ay, and ßy. c) Is P(X) commutative? Justify your answer. d) Give the matrices for Ta, Tg, and T, in terms of the standard basis vectors e,, e2, ez and e4 of R4.

2 3 4 1 4 3 2 3 4 1) 1 2 2. Let X = {1,2, 3, 4}. Consider the following elements of P(X): a = (; 2 3 4 (1 2 3 4 y = \1 3 4 2 a) How many elements are in the group P(X)? b) Calculate aß, ay, and ßy. c) Is P(X) commutative? Justify your answer. d) Give the matrices for Ta, Tg, and T, in terms of the standard basis vectors e,, e2, ez and e4 of R4.

Advanced Engineering Mathematics
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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2. Let X = {1,2, 3, 4}. Consider the following elements of P(X): a = (; (1 2 3 4 1 4 3 2 1 2 3 4 1) 2 3 4 (1 2 3 4 y = \1 3 4 2 a) How many elements are in the group P(X)? b) Calculate aß, ay, and ßy. c) Is P(X) commutative? Justify your answer. d) Give the matrices for Ta, Tg, and T, in terms of the standard basis vectors e,, e2, ez and e4 of R4.
Transcribed Image Text:2. Let X = {1,2, 3, 4}. Consider the following elements of P(X): a = (; (1 2 3 4 1 4 3 2 1 2 3 4 1) 2 3 4 (1 2 3 4 y = \1 3 4 2 a) How many elements are in the group P(X)? b) Calculate aß, ay, and ßy. c) Is P(X) commutative? Justify your answer. d) Give the matrices for Ta, Tg, and T, in terms of the standard basis vectors e,, e2, ez and e4 of R4.
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