I Question regarding actual computation of tensor at point (Self Study)

Amateur659
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Hello all,

I am hoping to get some feedback on the manner in which I performed computations towards solving the following problem.

question.PNG


There are a couple specific points which I am not confident of:
1. Did I properly account for the manifold structure in my computation of the nonzero components?
2. Is the general process by which I compute each tensor component correct?
IMG_20220213_010056272.jpg


Finally, please let me know if I am making a mistake posting such questions here.

Thank you for your time and feedback!
 

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It looks fine.
 
Awesome, thanks for the feedback.
 

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