In this case, we calculate (adj A) B If (adj A) B ≠ O, (O being zero matrix), then solution does not exist and the
system of equations is called inconsistent Rationalised 2023-24
DETERMINANTS     95
If (adj A) B = O, then system may be either consistent or inconsistent according
as the system have either infinitely many solutions or no solution Example 16 Solve the system of equations
2x + 5y = 1
3x + 2y = 7
Solution The system of equations can be written in the form AX = B, where
A =
2
5
1
,X
and B
3
2
7
x
y


 
 
=
=


 
 


 
 
Now, A  = –11 ≠ 0, Hence, A is nonsingular matrix and so has a unique solution