Question

4. (15 pts) Tensors \(\tau\) and \(\sigma\) are symmetrical and anti-symmetrical, respectively. Use index notations to show \(\tau : \sigma = 0\) Hint: There are several ways to prove the resulting term is a zero. You may consider expanding the final expression you get from the index notation approach, and see if they sum up to be a zero. Or you may opt for using a very commonly adopted approach to prove \"something is zero\" E.g., if you want to show \(A = 0\); you could firstly say \(A = (1/2)A + (1/2)A\) (always true). If you can find a way to turn the equation into \(A = (1/2)A -\ (1/2)A\), this nicely shows that \(A = 0\) (as \((1/2)A - (1/2)A = 0\).

          4. (15 pts)
Tensors \(\tau\) and \(\sigma\) are symmetrical and anti-symmetrical, respectively. Use index notations to
show \(\tau : \sigma = 0\)
**Hint:** There are several ways to prove the resulting term is a zero. You may consider expanding the final
expression you get from the index notation approach, and see if they sum up to be a zero. Or you may opt for
using a very commonly adopted approach to prove \"something is zero\" E.g., if you want to show \(A = 0\); you
could firstly say \(A = (1/2)A + (1/2)A\) (always true). If you can find a way to turn the equation into \(A = (1/2)A -\
(1/2)A\), this nicely shows that \(A = 0\) (as \((1/2)A - (1/2)A = 0\).

4. (15 pts)
Tensors τ and σ are symmetrical and anti-symmetrical, respectively. Use index notations to
show τ : σ = 0
**Hint:** There are several ways to prove the resulting term is a zero. You may consider expanding the final
expression you get from the index notation approach, and see if they sum up to be a zero. Or you may opt for
using a very commonly adopted approach to prove s̈omething is zeroË.g., if you want to show A = 0; you
could firstly say A = (1/2)A + (1/2)A (always true). If you can find a way to turn the equation into A = (1/2)A -(1/2)A, this nicely shows that A = 0 (as (1/2)A - (1/2)A = 0.

Added by Sarah P.

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