? ? 8. Let F be a field and n a positive integer. The (lower) triangular group
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8. Let F be a field and n a positive integer. The (lower) triangular group Tr (n, F) is the subgroup of all matrices (aij) in GL(n, F) with aij = 0 whenever i Hints: Note first that Tr (n, F)' Tri(n, F) if |F > 2 and Tr (n, F) = Tri(n, F) if |F| = 2. Let (aij) and (bij) lie in Tri(n, F) with dij = 0 for 0 < i j < r and bij 0 for 0i- j < s. Set (Cij) = [(aij), (bij)]. Prove that Cij 0 for 0i- j < r + s. = = 8. Let F be a field and n a positive integer. The (lower) triangular group Tr (n, F) is the subgroup of all matrices (aij) in GL(n, F) with aij = 0 whenever i Hints: Note first that Tr (n, F)' Tri(n, F) if |F > 2 and Tr (n, F) = Tri(n, F) if |F| = 2. Let (aij) and (bij) lie in Tri(n, F) with dij = 0 for 0 < i j < r and bij 0 for 0i- j < s. Set (Cij) = [(aij), (bij)]. Prove that Cij 0 for 0i- j < r + s. = =
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Related Book For
Probability and Statistics
ISBN: 978-0321500465
4th edition
Authors: Morris H. DeGroot, Mark J. Schervish
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