(Solution) - a Given the components of a 20 tensor M as -(2025 Original AI-Free Solution)

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(a) Given the components of a (20) tensor M?? as the matrix

find:
(i) The components of the symmetric tensor M(??) and the antisymmetric tensor M[??];
(ii) The components of M??;
(iii) The components of M??;
(iv) The components of M?? .
(b) For the (11) tensor whose components are M??, does it make sense to speak of its symmetric and antisymmetric parts? If so, define them. If not, say why.
(c) Raise an index of the metric tensor to prove
??? = (?(.