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10 Nov 2019
8, Recall GL (n, R) is the group consisting of all matrices, X, with real number entires and det(X) 0. Determine if the following are subgroups of GL(n, R). If they are, prove that you are correct. If they are not, explain why. Hint: the following properties of determinants might be heipful. det(AB) = det(A) det(B) and det (A-1)-det(A) (a) The set of all n à n matrices with real number entires and determinant 1. (b) The set of all n x n matrices with real number entires and determinant -1. (c) The set of all n à n matrices with real number entires and integer determinants.
8, Recall GL (n, R) is the group consisting of all matrices, X, with real number entires and det(X) 0. Determine if the following are subgroups of GL(n, R). If they are, prove that you are correct. If they are not, explain why. Hint: the following properties of determinants might be heipful. det(AB) = det(A) det(B) and det (A-1)-det(A) (a) The set of all n à n matrices with real number entires and determinant 1. (b) The set of all n x n matrices with real number entires and determinant -1. (c) The set of all n à n matrices with real number entires and integer determinants.
Deanna HettingerLv2
26 Sep 2019