# Matrices

Definition: A matrix (or matrices in plural) is a set of values organized into columns and rows and enclosed in brackets:

This matrix, Matrix A, has two rows and two columns, so is called a “2 by 2”, or 2×2 matrix (where dimensions are described as rows x columns.)

Each entry or element in a matrix has an address describing its location. This location is written as the lower case matrix letter followed by the element’s row number and column number in subscript. For example, in the matrix above, the element b is in row 1, column 2 of matrix A, so it’s location is described as a₁₂ .

Example: Give the dimensions of the matrix and describe the location of the element 0:

Solution:

Step 1: Recall that matrix dimensions are written as (number of rows x number of columns)

This matrix has 2 rows and 3 columns, so it’s dimensions are 2×3.

Step 2: Recall that the location of an entry is written as the lower case matrix letter followed by the element’s row number and column number in subscript.

To write the location of the 0 in this matrix, we observe that it is in matrix B, row 2, column 2. This address can be written as b₂₂