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We consider the set G of 3 x 3 matrices with coefficients in Z2 defined as follows: 1 ab G:= | a, b, c€ Z2. 0 0 1 (a) Show that G is a subgroup of GL3(Z2). What is its order? (b) Show that the following two elements A, BEG do not commute: A := 0 ī O 0 0 1 B:= 0 ī ī 0 0 T Is G a cyclic group? (c) Show that G is generated by A and B.

We consider the set G of 3 x 3 matrices with coefficients in Z2 defined as follows: 1 ab G:= | a, b, c€ Z2. 0 0 1 (a) Show that G is a subgroup of GL3(Z2). What is its order? (b) Show that the following two elements A, BEG do not commute: A := 0 ī O 0 0 1 B:= 0 ī ī 0 0 T Is G a cyclic group? (c) Show that G is generated by A and B.

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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Problem 1. We consider the set G of 3 x 3 matrices with coefficients in Z2 defined as follows: 1 a b { | a, b, ce Z,. G := 01c 0 0 1 (a) Show that G is a subgroup of GL3(Z2). What is its order? (b) Show that the following two elements A, B EG do not commute: A := B:= 0 ī ī Is G a cyclic group? (c) Show that G is generated by A and B.
Transcribed Image Text:Problem 1. We consider the set G of 3 x 3 matrices with coefficients in Z2 defined as follows: 1 a b { | a, b, ce Z,. G := 01c 0 0 1 (a) Show that G is a subgroup of GL3(Z2). What is its order? (b) Show that the following two elements A, B EG do not commute: A := B:= 0 ī ī Is G a cyclic group? (c) Show that G is generated by A and B.
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