### 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}\)

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}\)