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## Homework Statement

Find the dual vector of the following tensor:

6 3 1

4 0 5

1 3 2

## Homework Equations

dj= EijkTik

Where Eijk = 1 if ijk=123, 231, 312

Eijk = 0 if i=j i=k or j=k

Eijk = -1 if ijk = 132, 213, 321

## The Attempt at a Solution

Ok, so I'm not really sure how to solve this but my thought is that it is simply multiply diagonally across the matrix such that

dj= (6*0*2)*(1) + (3*5*1)(1) +(1*4*3)*(1) + (1*0*1)(-1) + (6*5*3)(-1) +(3*4*2)(-1)

However, I don't see how that gets me a vector in the end.

Please HELP!