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Problem #1: A rank two tensor L is given as: 7 10 3 L = L =4 -1 -2 9 4 5 (a) Calculate the symmetric (S) and skew-symmetric or antisymmetric (W) parts. (b) Calculate the three invariants of S and W tensors. (c) Show the following: (i) tr(SW) = 0 (ii) det(S') = det(S) (ii) det(S) = (detS)

Problem #1: A rank two tensor L is given as: 7 10 3 L = L =4 -1 -2 9 4 5 (a) Calculate the symmetric (S) and skew-symmetric or antisymmetric (W) parts. (b) Calculate the three invariants of S and W tensors. (c) Show the following: (i) tr(SW) = 0 (ii) det(S') = det(S) (ii) det(S) = (detS)

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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Problem #1: A rank two tensor L is given as: 7 10 L = L =|4 -1 -2 9 4 5 (a) Calculate the symmetric (S) and skew-symmetric or antisymmetric (W) parts. (b) Calculate the three invariants of S and W tensors. (c) Show the following: (i) tr(SW) = 0 (ii) det(s") = det(S) (iii) det(S)= (detS)! Problem #2: Prove the following relationship of second rank tensors: = 8, do, do (b) S
Transcribed Image Text:Problem #1: A rank two tensor L is given as: 7 10 L = L =|4 -1 -2 9 4 5 (a) Calculate the symmetric (S) and skew-symmetric or antisymmetric (W) parts. (b) Calculate the three invariants of S and W tensors. (c) Show the following: (i) tr(SW) = 0 (ii) det(s") = det(S) (iii) det(S)= (detS)! Problem #2: Prove the following relationship of second rank tensors: = 8, do, do (b) S
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