4 In parts ac state whether the equations below make correct

4. In parts (a)-(c) state whether the equations below make correct or incorrect use of index notation. If the notation is incorrect, briefly state why it is incorrect. If there is more than one mistake, list all of them. (a) oui oui n oui ouk Oki ori or (b) oai oble ore ori (c) odi od O2cij Obi ajkaak t Eiki are (aii) v v Oak Oak arkdak

Solution

(a) INCORRECT use of index notation:

Second term is wrong with respect to the index k. The left hand side of the equation does not contain the index k and k appears as a free index in the second term.

(b) This is CORRECT use of the index notation as i is the only variable and the summation of dummy indices j,k,l is accounted for in each term.

(c) INCORRECT use of index notation: i is a free variable on the left hand side but appears as a dummy index in the third term