Suppose that A is a covector field, and consider the object = (a) Show explicitly that F, is a tensor, that is, show that it transforms appropriately under a coordinate transformation. (b) Show that the definition F₁ = VA-VA, which uses the covariant derivative, is equiv- alent to the definition above.

Suppose that A is a covector field, and consider the object = (a) Show explicitly that F, is a tensor, that is, show that it transforms appropriately under a coordinate transformation. (b) Show that the definition F₁ = VA-VA, which uses the covariant derivative, is equiv- alent to the definition above.