Determinants

Determinants


Determinants are used to solve equations. Simultaneous equations can easily be solved by this. A determinant has elements inside two vertical bars.


Determinant of second order


A second order determinant looks like this



A second order determinant has two columns and two rows. The two columns of the elements are placed between two bars. The elements are a1, a2, b1 and b2.


The value of the determinant is

If we consider two simultaneous equations


a1 x + a2 y = a3

b1 x + b2 y = b3


Then we solve the simultaneous equations like



Determinant of third order


A third order determinant looks like this



A third order determinant has three columns and three rows. The three columns of the elements are placed between two bars. The elements are a1, a2, a3, b1 ,b2 , b3, c1, c2 and c3.


The value of the determinant is



If we consider three simultaneous equations

a1x + a2y + a3z = a4

b1x + b2y + b3z = b4

c1x + c2y + c3z = c4







Determinants





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