Normal form of a matrix

                            

             Normal form 

Every mxn read as (m by n) matrix of rank r can be reduced to form Ir, [Ir 0] by a finite chain of elementary row or column operations, where Ir is the rowed unit matrix.
The above form is called "normal form" or "fist canonical form" of a matrix.



Condition 1: The rank of a mxn matrix A is r if and only if it can be reduced to the form 

by a finite chain of elementary row and column operations.

Condition 2: If A is an mxn matrix of rank r, there exists non-singular matrices P and Q such that 

Example problem of Normal form:

  Therefore Rank(A) = 3.
Link for video lecture: https://youtu.be/a1NLzqvo8Nc