#### Introduction

- Each element in a matrix can be uniquely referred to by its position.
- Each element is appended a subscript containing its row position and column position respectively.
- For example:

refers to the element in row 2, column 1`x`

_{21}

- For example:
- The index of the row or column always starts at 1 (as opposed to programming where it starts at 0).

#### Example

#### LaTeX

```
\begin{bmatrix}
x_{11} & x_{12} & x_{13} & \dots & x_{1n} \\
x_{21} & x_{22} & x_{23} & \dots & x_{2n} \\
\hdotsfor{5} \\
x_{d1} & x_{d2} & x_{d3} & \dots & x_{dn}
\end{bmatrix}
```

#### code (Python)

Note that we access element x_{21}, however we refer to it as a[1, 0] because in programming indexes start at 0, not 1.

```
import numpy as np
a = np.matrix([[3, 6, 2], [5, 1, 10]])
print(a) # prints [[ 3 6 2]
# [ 5 1 10]]
print(a[1, 0]) # prints '5'
a[1, 0] = 3
print(a[1, 0]) # prints '3'
```