Theory:

Let us consider the data given below and try to represent the same in the tabular column.
 
In a unit test, the students scored the following.
 
(i) Dev scored \(75\%\) in English, \(60\%\) in Science, and \(80\%\) in Mathematics.
 
(ii) Athitya scored \(65\%\) in English, \(85\%\) in Science, and \(82\%\) in Mathematics.
 
(iii) Gautham scored \(85\%\) in English, \(68\%\) in Science, and \(70\%\) in Mathematics.
 
Let us now try to represent the information gathered in the form of a tabular column.
 
Here, the numbers entered to represent the percentage scored in each of the subjects.
 
Name
English
Science
Mathematics
Dev
\(75\)
\(60\)
\(80\)
Athitya
\(65\)
\(85\)
\(82\)
Gautham
\(85\)
\(68\)
\(70\)
 
Let us now look at the alternate way of representing the same information.
 
\(\begin{bmatrix}
75 & 60 & 80\\ 
65 & 85 & 82\\ 
85 & 68 & 70
\end{bmatrix}\)
 
We have represented the same data in rows and columns, which is the matrix form.
 
The horizontal representations are the rows, and the vertical representations are the columns.
 
Matrix:
A matrix is a rectangular array of elements represented in the form of horizontal rows and vertical columns.
pic1.svg
 
How matrices are formed?- A real life example
Example:
Let us look at a few examples of matrices.
 
1. \(\begin{bmatrix}
-5 & 3 & 10\\ 
9 & -4 & 2\\ 
\sqrt{4} & 68 & 21
\end{bmatrix}\)
 
2. \(\begin{bmatrix}
\frac{1}{2} & -8 & 3\\ 
0 & -\frac{4}{9} & 7\\ 
\frac{\sqrt{2}}{3} & 14 & 10
\end{bmatrix}\)
 
3. \(\begin{bmatrix}
x^2 & 5\\ 
3x + 1 & 0
\end{bmatrix}\)