Determinants

• For any four numbers, a, b, c and d, the value ad – bc can be represented as . This type of representation of numbers or variables is called determinant. It is a determinant of order two.

• Cramer’s rule:

For two simultaneous equations, a1x + b1y = c1 and a2x + b2y = c2 where a1, a2, b1, b2, c1 and c2 are real numbers such that a1b2 – a2b1 ≠ 0 and x and y are variables then:

 x = and y =

Here, D = , Dx =  and Dy =

Determinant of a square matrix A is denoted by or det (A). Determinant of a matrix Determinant of a matrix is given by, Determinant of a matrix  is given by (expanding along R1):

 

Similarly, we can find the determinant of …