# Introduction to Matrices

### INTRO

A matrix is simply an array of numbers, and we usually denote it by a capital letter.

$\text{e.g}. \quad A = \begin{bmatrix} 5 & 1 & 7 \\ 2 & -1 & 3 \end{bmatrix} \\$
In general, we would have $$A = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{12} & \cdots & a_{2n} \\ \vdots & \vdots & & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \\ \end{bmatrix}$$. Notice that we refer to entries as $$a_{ij}$$ where $$i$$ is the row and $$j$$ is the column of the entry we are talking about. The size of the matrix is $$m \times n$$ where $$m$$ is the number of rows and $$n$$ is the number of columns.

Example: If $$A = \begin{bmatrix} 5 & 1 & 7 \\ 2 & -1 & 3 \end{bmatrix}$$, find $$a_{21}$$ , $$a_{13}$$, and determine the size of the matrix.

Solution:
There are 2 rows and three columns so the size of the matrix is 2 x 3. Also, $$a_{21} = 2$$ because this refers to the entry in the 2nd row and the 1st column. Finally, $$a_{13} = 7$$ because this refers to the entry in the 1st row and the 3rd column.