Matrices and Determinants Brahmagupta (c. AD(CE) - c. AD(CE)) XII Std - Business Maths & Stat EM Chapter - - . Rank of a Matrix Matrices are one of the most commonly used tools in many fields such as Economics, Commerce and Industry.
We have already studied the basic properties of matrices. In this chapter we will study about the elementary transformations to develop new methods for various applications of matrices. . .
Concept With each matrix, we can associate a non-negative integer called its rank. Definition . The rank of a matrix A is the order of the largest non-zero minor of A and is denoted by r ( ) In other words, A positive integer ‘ r ’ is said to be the rank of a non- zero matrix A , if (i) there is atleast one minor of A of order ‘ r ’ which is not zero and (ii) every minor of A of order greater than ‘ r ’ is zero. (i) r ( ) A ≥ (ii) If A is a matrix of order m then r ( ) A £ minimum of m n