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1 Write A =-1 1 0 as a product of an element of O(3) and an element of 0 0 1 B, (R).

1 Write A =-1 1 0 as a product of an element of O(3) and an element of 0 0 1 B, (R).

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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Please answer 4a. If you don't know the answer let the others do it.

Here O(3) is orthogonal matrix of order 3

and B3(R) is any matrix or order 3

A Prove that a group G of order 24 must have a normal subgroup of order 4 or 8. [Hint: Consider a Sylow 2-subgroup P of G, and the action of G on the cosets G/P.] 0 1 4. a) Write A = -1 1 0| as a product of an element of O(3) and an element of 1 B,(R). Give an example, with justification, of an abelian group of rank 7 and with torsion group being non-cyclic of order 8.
Transcribed Image Text:A Prove that a group G of order 24 must have a normal subgroup of order 4 or 8. [Hint: Consider a Sylow 2-subgroup P of G, and the action of G on the cosets G/P.] 0 1 4. a) Write A = -1 1 0| as a product of an element of O(3) and an element of 1 B,(R). Give an example, with justification, of an abelian group of rank 7 and with torsion group being non-cyclic of order 8.
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