MATRICES
The concept of matrices was developed by a Mathematician Arthur Cayley . Matrices are useful in expressing numerical information in compact form. They are effectively used in expressing different operators . Definition : A rectangular arrangememnt of mn numbers in m rows and n columns, emclosed in [ ] or ( ) is called a matrix of order m by n . A matrix by itself does not have a value or any special meaning . Order of the matrix is denoted by m m🗙n , read as m by n . Each member of the matrix is called an element of the matrix . Matrices are generaly denoted by A, B, C, ... and their elements are denoted by a ij , b ij , c ij , ...etc. Matrix is generaly written as : Important Formulas for Matrices If A and B are square matrices of order n, and I n is a corresponding unit matrix , then (a) A(adj.A) = | A | I n = (adj A) A (b) | adj A | = | A |n -1 (Thus A (adj A) is always a scalar matrix) (c) adj (adj.A) = | A | n-2 A (d) adj (AB) = (adj B) (adj A) (e) adj (A m