# Array

An array is an arrangement of objects, such as numbers, typically in rows and/or columns. A table is a common example of an array.

Column 1 | Column 2 | Column 3 | |
---|---|---|---|

Row 1 | 1,1 | 1,2 | 1,3 |

Row 2 | 2,1 | 2,2 | 2,3 |

Row 3 | 3,1 | 3,2 | 3,3 |

Row 4 | 4,1 | 4,2 | 4,3 |

Row 5 | 5,1 | 5,2 | 5,3 |

The table above shows a basic array with 5 rows and 3 columns. The pair of numbers in each cell indicates what row and what column that cell represents, with the first number indicating the row and the second number indicating the column. For example, the "1,2" indicates "row 1, column 2," which we can see is true based on the column and row labels on the table.

Tables can, and typically do contain more than just numbers. They can contain virtually anything you want to put in them, but regardless what is in the cells, a given cell would be referred to in the same way as shown in the table.

## Arrays in mathematics

Arrays are used in many different areas, not just mathematics, but this page focuses on arrays in mathematics. Below are a few examples.

### Multiplication charts

One example of an array in math is a multiplication chart.

× | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 |

3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 |

4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 |

5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 |

6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 |

7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 |

8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 |

9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 |

In the multiplication chart, the values in the first row and column represent which two values to multiply dependent on which cell of the chart we are looking at. For example, cell 7,5 represents the multiplication problem 7 × 5, and the value in cell 7,5 is the result of that multiplication: 35.

### Matrices

Matrices are not a primary math topic, but if you look at an example of a matrix, you will see that it is also an array. There are many different ways to represent a matrix. One common way is to have an array of values within brackets.

There are a number of ways to refer to a matrix and its elements, or the objects in the matrix (in this case numbers). Generally, elements can be referred to in the same manner as the cells in a table - based on the row and column that the element occupies.