Chapter 10.5, Problem 1P

Verify that (5.5) agrees with a Laplace development, say on the first row (Chapter 3, Section 3). Hints: You will find 6 terms corresponding to the 6 non-zero values of ${ϵ}_{ijk}.$ First let $i=1;$ then j, k can be 2,3 or 3,2. These two terms give you $a_{11}$ times its cofactor. Next let $i=2$ with $j,k=1,3$ and 3,1, and show that you get $a_{12}$ times its cofactor. Finally let $i=3.$ Watch all the signs carefully.