Given system of equations is
5x + 2y =4
7x + 3 y = 5
Writing the given system of equations in matrix form
AX = B …….(1)
Determinant of matrix |A| is
= 5 x 3 – 7 x 2 = 15 – 14 = 1
∴ |A| = 1 ≠ 0
Since, matrix A is non-singular so A-1 exists and system is consistent.
If Aij is cofactor of a in Aij, then
A11 =(-1)1+1(3) = 3
A12 =(-1)1+2 = 7 = -7
A21 =(- 1)2+1 (2) = -2
A22 = (1)2+2 (5) = 5
Matrix formed by the cofactors of |A| is
