... =(–1)N(1,2 ,3) a11a22a 33 +(–1)N(1 ,3, 2)a11a 32 a 23 +(–1)N(2,1 ,3) a21a12a 33 +(–1)N(2 ,3, 1)a21a 32 a 13 +(–1)N (3, 1,2)a 31 a12a 23 +(–1)N (3, 2,1)a 31 a22a 13 =(–1)0×1×1×(–4)+(–1)1×1×(–1) ×5+(–1)1×6×(–1) ... third-order determinant of the matrix from Exam-ple 1. The numbers β1, β2, β 3 represent permutations of the set 1, 2, 3. WehaveΔ ≡ det A =(–1)N(1,2 ,3) a11a22a 33 +(–1)N(1 ,3, 2)a11a 32 a 23 +(–1)N(2,1 ,3) a21a12a 33 +(–1)N(2 ,3, 1)a21a 32 a 13 +(–1)N (3, 1,2)a 31 a12a 23 +(–1)N (3, 2,1)a 31 a22a 13 =(–1)0×1×1×(–4)+(–1)1×1×(–1) ... xn–1n=1≤j<i≤n(xi– xj).5.2. 2-6 . Determinant of a sum and a product of matrices.The determinant of the product of two matrices A and B of the same size is equal to theproduct of their determinants,det(AB)=detA...