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
|
No |
Starting place |
Destination |
|
1 |
Mangaluru |
Mumbai |
|
2 |
Mangaluru |
Pune |
|
3 |
Hubballi |
Pune |
|
4 |
Belagavi |
Nagapura |
|
5 |
Mumbai |
|
|
6 |
Mumbai |
|
|
7 |
Pune |
|
|
8 |
Pune |
|
|
9 |
Pune |
Vadodara |
|
10 |
Nagapura |
|
|
11 |
Nagapura |
Vadodara |
Can you tell quickly the number of direct connection
between Mangaluru and
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:
A= 
|
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. |
B=
|
3.4 Summary of learning
|
No |
Points
studied |
|
1 |
Definition
of matrix, rows, columns, order |
