Solution In general a 3 × 2 matrix is given by 
11
12
21
22
31
32
A
a
a
a
a
a
a




= 




 Now
1 |
3 |
2
aij
i
j
=
−
, i = 1, 2, 3 and  j = 1, 2 Therefore
11
1 |1 3 1|
1
2
a
=
− ×
=
12
1
5
2|1 3 2|
2
a
=
− ×
=
21
1
1
| 2
3 1|
2
2
a
=
− ×
=
22
1 | 2
3 2|
2
2
a
=
− ×
=
31
1 |3
3 1|
0
2
a
=
− ×
=
32
1
3
|3
3 2 |
2
2
a
=
− ×
=
Hence the required matrix is given by 
5
1
2
1
A
2
2
3
0
2






= 






 Rationalised 2023-24
MATRICES         39
3