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 Note that
A–1 = −
−
−




1
11
2
5
3
2
Therefore
X = A–1B = – 1
11
2
5
3
2
71
−
−








i