How Does the Cross Product Relate to Rank 1 Tensors?

[zorrorojo]

Homework Statement

I don't know how to prove it.
Let us consider two arbitrary vectors
⃗ A and ⃗B.
Let us define the vector product of them as
⃗C = ⃗A × ⃗B
Show that the vector ⃗C belongs to the Rank 1 tensor. In other words,
prove that
C′i = λij Cj
where
Ci ≡ ϵij k Aj Bk
C′i ≡ ϵijk A′j B′k

Homework Equations

The Attempt at a Solution

I just tried, but I don't know about it.

 

[gabbagabbahey]

The Attempt at a Solution

I just tried, but I don't know about it.

Hi zorrorojo, welcome to PF!

You'll need to be more specific than "I just tried, but I don't know about it" in order to get assistance here.

What exactly did you try? Show your attempt.

 

[sinanfe]

pls answer these qoestion:
1)expand the following
aibj ϵijk=
ϵjkl (du,l/dx,k)