General coordinate transformations for tensors

[Deadstar]

Homework Statement

Write down the transformation laws under general coordinate transformations for a
tensor of type (0,1) and a tensor of type (2,1) respectively

The Attempt at a Solution

I seem to have two transformation formulas but they could in fact just be the same thing. I'll just do the (0,1) tensor.

So, is the answer...

V_a' = \frac{\partial x^k}{\partial {x'}^a} V_k

or is it

x_a' = x_a'(x_b)

Or are these just the same thing?

This is probably a trivial question but just got to make sure

 

[fzero]

The first formula you wrote describes how the tensor V_k transforms under the change of coordinates in the 2nd formula. So the first formula is part of what you need to answer the question.