Prove that curl of a vector is a vector

[SSDdefragger]

Homework Statement

Proove it

Iam supposed to change coordinate system, and proove that the result depends on coordinate system.

The Attempt at a Solution

My attempt was to start from definition of cross product using levicivita. I already prooved that divergence of a vector is a scalar. But when I am trying the same approach I am getting confused with indices (i don't know where do i have to put the same index where i dont)

 

[vela]

What does it mean specifically to prove something is a vector?

Please show your work. We can't help you unless we can see what you did. Generic descriptions aren't that useful.