Matrices:

 A rectangular array of symbols (which may be complex or real numbers) along columns and rows is known as matrix.

Therefore a system of m ´ n symbols given in a rectangular creation along m rows and n columns and surrounded by the brackets [.] is known as an m by n matrix (which is defined as m x n matrix).

Therefore                                   

Determinants:

• Suppose the equations a₁x+b₁y = 0 and a₂x+b₂y = 0. These provides

We express that eliminate as = 0.

• 
• A determinant of order three having of 3 rows and 3 columns is shown as   and is same to

The numbers a_i, b_i, c_i  ( i =1,2,3 ) are known as the elements of the determinant.

The determinant calculating by removing the ith row and jth column is known as the minor of the component at the ith row and the jth column. The co-factor of this component is (-1)^i+j  (minor). 

      Noticed that : Δ = = a₁A₁ + b₁B₁+c₁C₁

      where A₁, B₁ and C₁ are the co-factors of a₁, b₁ and c₁ respectively. i.e., the addition of products of the components of any row (column) of a determinant with the related co-factors is same to the value of the determinant.

We may expand the determinant through any column or row. It denotes that we may write:

These expression are true for determinants of any order.

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