Question: Let (T^{alpha}) be a contravariant vector and (S_{alpha}) be a covariant vector. a. Show that (R_{beta}=g_{alpha beta} T^{alpha}) is a covariant vector. b. Show that

Let \(T^{\alpha}\) be a contravariant vector and \(S_{\alpha}\) be a covariant vector.

a. Show that \(R_{\beta}=g_{\alpha \beta} T^{\alpha}\) is a covariant vector.

b. Show that \(R^{\beta}=g^{\alpha \beta} S_{\alpha}\) is a contravariant vector.

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