Δr consists of (n – 1) determinants in L.H.S. and in R.H.S every constituent of first row consists of (n – 1) elements and hence it can be splitted into sum of (n – 1) determinants.
∴
n−1
∑
r=1
Δr=|
n(n−1)
2
(n−1)2
(n−1)(3n−4)
2
n
2
n−1
a
n(n−1)
2
(n−1)2
(n−1)(3n−4)
2
|=0
(∵R1 and R3 are identical) Hence, value of
n−1
∑
r=1
Δr is independent of both and a'and'n'n′ a'and'n'$