Matrices

Introduction

     It is a rectangular array of numbers, arranged in rows and columns.

     The number of rows (say m) and the number of columns (say n) determine the order of the matrix. It is written as m x n (to be read as m by n).

     The plural of matrix is matrices. Matrix is usually denoted by capital letters such as A, B, C,…

     The Types of Matrices are: square matrix, row matrix, column matrix, zero matrix or a null matrix.

Equality of Matrices

     If two matrices have their corresponding elements equal, then they are called equal matrices.

      Two equal matrices are exactly the same.
If the given matrix A is of the order m x n, then its transpose will be of the order n x m.

Addition of Matrices

     To add two matrices:

     (i) Check whether they are of the same order.

     (ii) If they are of the same order, add the corresponding elements.

     (ii) It will be seen that the matrix obtained after addition will also be a matrix of the same order.

Subtraction of Matrices

     Two matrices can be subtracted in the same way as they are added. We change the signs of the corresponding elements and then add them.

Multiplication of a Matrix by a Scalar

     When a matrix is multiplied by a scalar factor k, then each element of the matrix is multiplied by k.

Some properties of Addition and Subtraction of Matrices

     The Properties of Matrices are: Commutative property, Distributive property, Associative property, additive inverse property. Zero matrix possesses identity property of addition.

Multiplication of Matrices

     Two matrices A and B can be multiplied if the number of columns of A is equal to the number of rows of B. The resultant matrix will be of the order of (number of rows of A x number of columns of B).

     If A be a matrix of the order m x n and B be a matrix of the order n x q, then A and B can be multiplied and the product will be a matrix of order m x q.

     Elements of rows of matrix A are multiplied by the corresponding elements of columns of B and we get AB.

Summary

     1. A matrix is a rectangular array of numbers, arranged in rows and columns.

     2. Order of a matrix = Number of rows in it x Number of columns in it

     3. Row matrix is a matrix with only one row.

     4. Column matrix is a matrix with only one column.

     5. Zero or Null matrix is a matrix in which every element is zero.