Question

Let `{D_1, D_2, D_3 ,D_n}` be the set of third order determinant that can be made with the distinct non-zero real numbers `a_1, a_2, a_qdot` Then `sum_(i=1)^n D_i=1` b. `sum_(i=1)^n D_i=0` c. `D_i-D_j ,AAi ,j` d. none of these
A. `overset(n)underset(i=1)(Sigma) D_(i)=1`
B. `overset(n)underset(i=1)(Sigma)D_(i)=0`
C. `D_(i)D_(j), AA I, j`
D. None of these

Answer 1

Correct Answer - B
the total number of third -order determinants is 9! The number of determinants s even and of these there are `9!//2` pairs of determinants which are obtained by changing two consecutive
`" rows so " overset(n)underset(i=1)(Sigma) D_(i) =0`