3

3.4 Introduction to Matrices:

This branch of mathematics is useful in the study of Science, Engineering, Economics and other fields.

The 11 railway connections between cities of Karnataka, Maharashtra and Gujarat is as follows

No	Starting place	Destination
1	Mangaluru	Mumbai
2	Mangaluru	Pune
3	Hubballi	Pune
4	Belagavi	Nagapura
5	Mumbai	Ahmadabad
6	Mumbai	Surat
7	Pune	Ahmadabad
8	Pune	Surat
9	Pune	Vadodara
10	Nagapura	Surat
11	Nagapura	Vadodara

Can you tell quickly the number of direct connection between Mangaluru and Ahmadabad and between Belagavi and Vadodara? The right answer is 2 and I respectively!

We will solve this problem in chapter 3.6

Let us read the following paragraph.

On Monday the attendance in your class was 30 girls and 22 boys and seven were absent. On Tuesday the attendance was 28 girls and 26 boys and 5 were absent. On Wednesday the attendance was 26 boys and 27 girls and six were absent. Thursday was a republic day and there were no classes. On Friday the attendance was 30 boys and 23 girls and six were absent. On Saturday the attendance was 34 boys and 24 girls and one was absent.

From the above data can you easily answer following questions?

1. Which day had maximum attendance?

2. Which day had maximum absentees?

3. On which day girls’ attendance was more than boys?

4. For how many days was girls’ attendance more than boys?

Since the data was in narration form, it was not that easy to answer these questions. Let us represent the data in a tabular form as shown below:

In this representation

1. The numbers in six horizontal rows represent attendance details for a week from Monday to Saturday.

2. The numbers in the first vertical column represent the attendance of girls for six days.

3. The numbers in the second vertical column represent the attendance of boys for six days.

4. The numbers in the third vertical column represent the number of absentees for six days.

With the above representation, we can easily answer the questions:

1. Saturday had maximum attendance (only one student was absent)

2. Monday had maximum absentees (7)

3. Monday had maximum attendance of girls

4. On three days (Monday, Tuesday and Wednesday) attendance of girls was more than that of boys

Definition : A ‘matrix’ is a rectangular representation of data in rows and columns, normally enclosed within brackets.

Definitions:

Each number or entity in a matrix is called ‘element’

The horizontal representations are called ‘rows’.

The vertical representations are called ‘columns’.

In the Attendance example discussed above, Matrix A has 6 rows and 3 columns. It is called a 6 by 3 (6X3) matrix.

The order of a matrix is denoted by (m x n), where m is number of rows and n is number of columns in the matrix.

In the adjacent Matrix B, the four sets of row elements are(p1,p2,p3),(q1,q2,q3),(r1,r2,r3) and(s1,s2,s3).

The three sets of column elements are (p1,q1,r1,s1),(p2,q2,r2,s2) and(p3,q3,r3,s3).

Thus matrix B has 4 rows and 3 columns and hence is a 4 by 3 (4X3) Matrix.

3.4 Summary of learning

No	Points studied
1	Definition of matrix, rows, columns, order