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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?

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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4. Let E denote the set of all 3 x 3 orthonormal matrices whose first column is (0, 1,0)T. (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 = -A? (What does this mean for the diagonal entries in A?) If there are, describe them all; if not, explain why not.
Transcribed Image Text:4. Let E denote the set of all 3 x 3 orthonormal matrices whose first column is (0, 1,0)T. (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 = -A? (What does this mean for the diagonal entries in A?) If there are, describe them all; if not, explain why not.
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