4. Let E denote the set of all 3 x 3 orthonormal matrices whose first column is (0, 1,0)". (a) Write down at least 2 matrices in E. (b) Are there any symmetric matrices in E, that is A such that AT = A? If there are, describe them all; if not, explain why not. (c) Are there any skew-symmetric matrices in E, that is A such that AT (What does this mean for the diagonal entries in A?) If there are, describe them all; if not, explain why not. - A?

4. Let E denote the set of all 3 x 3 orthonormal matrices whose first column is (0, 1,0)". (a) Write down at least 2 matrices in E. (b) Are there any symmetric matrices in E, that is A such that AT = A? If there are, describe them all; if not, explain why not. (c) Are there any skew-symmetric matrices in E, that is A such that AT (What does this mean for the diagonal entries in A?) If there are, describe them all; if not, explain why not. - A?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.1: Operations With Matrices

Problem 77E

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