36. Prove that the set of all 3 x 3 matrices with real entries of the form 1 0 0 01 b is a group. (Multiplication is defined by 1 a b 1 a' b' 36 61-6 c' 01 00 = 0 1 0 01 a 1 0 1 a+a' 1 0 b' + ac'+b c' + c 1 This group, sometimes called the Heisenberg group after the Nobel Prize-winning physicist Werner Heisenberg, is intimately re-

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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36. Prove that the set of all 3 X 3 matrices with real entries of the form
1
0
0
C
1
a
1
0
is a group. (Multiplication is defined by
1 a
b 1 a' b' 1
0 1
00
16
1 c' =
00 1
0
b
C
1
0
0
a+a'
1
0
b' + ac' + b
c' + c
1
This group, sometimes called the Heisenberg group after the
Nobel Prize-winning physicist Werner Heisenberg, is intimately re-
lated to the Heisenberg Uncertainty Principle of quantum physics.)
Transcribed Image Text:36. Prove that the set of all 3 X 3 matrices with real entries of the form 1 0 0 C 1 a 1 0 is a group. (Multiplication is defined by 1 a b 1 a' b' 1 0 1 00 16 1 c' = 00 1 0 b C 1 0 0 a+a' 1 0 b' + ac' + b c' + c 1 This group, sometimes called the Heisenberg group after the Nobel Prize-winning physicist Werner Heisenberg, is intimately re- lated to the Heisenberg Uncertainty Principle of quantum physics.)
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