... used exclusively in this and later chapters. However, many propertiesof particular determinants can be proved by performing a sequence of row and column operations and in these applications, the ... is,A p 1q1A p 1q2A p 2q1A p 2q2=0, 1 ≤ p 1 ,p 2,q1,q2≤ n.It follows thatA p 1q1A p 1q2A p 1q3A p 2q1A p 2q2A p 2q3A p 3q1A p 3q2A p 3q2=0since ... x1···xi−1nk=1aikekxi+1···xn=nk=1aik(x1···xi−1ekxi+1···xn)=nk=1aikAike1e2···en. (1.3.13)Determinants and Their Applications in Mathematical PhysicsRobert VeinPaul DaleSpringer1.4 The Product of Two Determinants — 1 5Comparing this result with (1.2.5),|aij|n=nk=1aikAik(1.3.14)which...