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2. Which of the following are groups? For those which are not groups, explain why not (it is enough to find one axiom that fails). For those which are, state the identity and inverses: (i) Q under x, (ii) {q Q:q> 0} under ×, (iii) {q Q:q>0} under division, (iv) {1, 2, 3, 4, 5, 6, 7} under x mod 8, (v) {1,3,5, 7) under × mod 8, (vi) {2, 4, 6, 8, 10, 12} under x mod 14, a -b b a (vii) 2 x 2 real matrices of the form both 0, (viii) The set {0,1,2,3,4,5} under the operation roy = |x+y - 5. under matrix multiplication, with a and b not

2. Which of the following are groups? For those which are not groups, explain why not (it is enough to find one axiom that fails). For those which are, state the identity and inverses: (i) Q under x, (ii) {q Q:q> 0} under ×, (iii) {q Q:q>0} under division, (iv) {1, 2, 3, 4, 5, 6, 7} under x mod 8, (v) {1,3,5, 7) under × mod 8, (vi) {2, 4, 6, 8, 10, 12} under x mod 14, a -b b a (vii) 2 x 2 real matrices of the form both 0, (viii) The set {0,1,2,3,4,5} under the operation roy = |x+y - 5. under matrix multiplication, with a and b not

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. Which of the following are groups? For those which are not groups, explain why not (it is enough to find one axiom that fails). For those which are, state the identity and inverses: (i) Q under x, (ii) {q Q:q>0} under ×, (iii) {q € Q: q> 0} under division, (iv) {1,2, 3, 4, 5, 6, 7) under x mod 8, (v) {1,3,5,7) under x mod 8, (vi) {2, 4, 6, 8, 10, 12} under × mod 14, a -b b a (vii) 2 x 2 real matrices of the form both 0, (viii) The set {0,1,2,3,4,5} under the operation roy = |x + y − 5|. under matrix multiplication, with a and b not
Transcribed Image Text:2. Which of the following are groups? For those which are not groups, explain why not (it is enough to find one axiom that fails). For those which are, state the identity and inverses: (i) Q under x, (ii) {q Q:q>0} under ×, (iii) {q € Q: q> 0} under division, (iv) {1,2, 3, 4, 5, 6, 7) under x mod 8, (v) {1,3,5,7) under x mod 8, (vi) {2, 4, 6, 8, 10, 12} under × mod 14, a -b b a (vii) 2 x 2 real matrices of the form both 0, (viii) The set {0,1,2,3,4,5} under the operation roy = |x + y − 5|. under matrix multiplication, with a and b not
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