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If the n x n matrices A and B are symmetric and B is in- vertible, which of the matrices in Exercises 13 through 20 must he symmetric as well? 13. ЗА 14. —В 15. AB 16. A+ B 17. В -1 18. A10 19. 21, + ЗА - 4A? 20. АВ?А

If the n x n matrices A and B are symmetric and B is in- vertible, which of the matrices in Exercises 13 through 20 must he symmetric as well? 13. ЗА 14. —В 15. AB 16. A+ B 17. В -1 18. A10 19. 21, + ЗА - 4A? 20. АВ?А

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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**Symmetric Matrices Exercises** *If the \( n \times n \) matrices \( A \) and \( B \) are symmetric and \( B \) is invertible, which of the matrices in Exercises 13 through 20 must be symmetric as well?* 13. \( 3A \) 14. \( -B \) 15. \( AB \) 16. \( A + B \) 17. \( B^{-1} \) 18. \( A^{10} \) 19. \( 2I_n + 3A - 4A^2 \) 20. \( AB^2A \)
Transcribed Image Text:**Symmetric Matrices Exercises** *If the \( n \times n \) matrices \( A \) and \( B \) are symmetric and \( B \) is invertible, which of the matrices in Exercises 13 through 20 must be symmetric as well?* 13. \( 3A \) 14. \( -B \) 15. \( AB \) 16. \( A + B \) 17. \( B^{-1} \) 18. \( A^{10} \) 19. \( 2I_n + 3A - 4A^2 \) 20. \( AB^2A \)
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