Now, this
system of equations has a unique solution or not, is
determined by the number a1 b2 – a2 b1 (Recall that if
1
1
2
2
a
b
a
≠b
 or, a1 b2 – a2 b1 ≠ 0,  then the system of linear
equations has a unique solution) The number a1 b2 – a2 b1
which determines uniqueness of solution is associated with the matrix 
1
1
2
2
A
a
b
a
b


= 



and is called the determinant of A or det A Determinants have wide applications in
Engineering, Science, Economics, Social Science, etc