### 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. 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. $$\begin{bmatrix} x^2 & 5\\ 3x + 1 & 0 \end{bmatrix}$$