Ambgiuous Summation Convention / Tensor Question

[Sephasa]

Hi everyone. So, I was set the question Simplify δ_(ij) a_(jk) b_(l) given that a_(ij) = 3 And the options: 1) 3b_(l) 2) a_(ik) b_(l) 3) a_(jk) b_(i) I picked option 2). But this was marked wrong, stating that 1) was correct. I can see the reasoning behind it, but is this question misleading/legal? Because j is used as a Dummy Index in one equation, but a Free Index in another?

 

[Deleted member 4993]

Hi everyone. So, I was set the question Simplify δ_(ij) a_(jk) b_(l) given that a_(ij) = 3 And the options: 1) 3b_(l) 2) a_(ik) b_(l) 3) a_(jk) b_(i) I picked option 2). But this was marked wrong, stating that 1) was correct. I can see the reasoning behind it, but is this question misleading/legal? Because j is used as a Dummy Index in one equation, but a Free Index in another?

I agree it is kind of confusing (not illegal - nobody is going to put anybody in jail) - but

it is a common practice to use (ij) in both the cases - since those are really dummy variables in both the cases.

I tend to avoid this but I allow for such double entendre.

 

[daon2]

I don't see how those answers are correct at all. There is no way to conclude any of the options is correct. Assuming delta is the dirac-delta function, (1) would be correct if i=j=k, (2) would be correct if i=j but j=/=k (otherwise you could simplify further).