Determinant of a matrix can be defined as a numerical value obtained from a square matrix of the coefficients of certain unknown variables enclosed by two bars by the process of diagonal expansion to tell upon a given algebraic system.

Consider the system of equations:

a_{11}x + a_{12}y = 0 a12x + a_{22}y = 0

Eliminating x and y, we get the expression as

a_{11}a_{22 }-a_{12}a_{21 }= 0