## Matrix Introduction

Matrices are everywhere. If you have used a spreadsheet program such as MS-Excel, Lotus or written a table (such as in Ms-Word) or even have used mathematical or statistical software such a Mathematica, Matlab, Minitab, SAS, SPSS and Eviews etc., you have used a matrix.

Matrices make the presentation of numbers clearer and make calculations easier to program. For example, the matrix is given below about the sale of tires in a particular store given by quarter and make of tires.

Q1 | Q2 | Q3 | Q4 | |

Tirestone | 21 | 20 | 3 | 2 |

Michigan | 5 | 11 | 15 | 24 |

Copper | 6 | 14 | 7 | 28 |

It is called matrix, as information is stored in particular order and different computations can also be performed. For example, if you want to know how many Michigan tires were sold in Quarter 3, you can go along the row ‘Michigan’ and column ‘Q3’ and find that it is 15.

Similarly, total number sales of ‘Michigan’ tiers can also be found by adding all the elements from Q1 to Q4 in Michigan row. It sums to 55. So, a matrix is a rectangular array of elements. The elements of a matrix can be symbolic expression or numbers. Matrix [A] is denoted by;

Row *i* of the matrix [*A*] has *n* elements and is [*a _{i1, }*

*a*, …

_{i2}*a*] and column of [

_{1n}*A*] has

*m*elements and is .

The size (order) of any matrix is defined by the number of rows and columns in the matrix. If a matrix [*A*] has *m* rows and *n* columns, the size of the matrix is denoted by (*m* x *n*). The matrix [*A*] can also be denoted by [*A*]* _{mxn }*to show that [

*A*] is a matrix that has

*m*rows and

*n*columns in it.

Each entry in the matrix is called the element or entry of the matrix and is denoted by *a _{ij}*, where

*i*represents the row number and

*j*is the column number of the matrix element.

The above-arranged information about sale and type of tires can be denoted by the matrix [*A*], that is, This matrix has 3 rows and 4 columns. So, the order (size) of the matrix is 3 x 4. Note that element *a _{23}* indicate the sales of tires in ‘Michigan’ in quarter 3 (Q3).