# Matrix Notation

Entry, Rows and Columns

A matrix is a way to organize data in columns and rows. A matrix is written inside brackets [ ]. Look at the picture below to see an example.
Each item in a matrix is called an entry.

### Example of a Matrix

The matrix pictured below has two rows and three columns.

• Its dimensions are 2 ×3
• 2 rows and three columns
• The entries of the matrix below are 2, -5, 10, -4, 19, 4.

### Dimension of Matrix

The dimensions of a matrix refer to the number of rows and columns of a given matrix. By convention the dimension of a a matrix are given by number of rows • number of columns

One way that some people remember that the notation for matrix dimensions is rows by columns (Rather than columns by rows) is by recalling a once popular-soda:


RC Cola	-- rows before columns!


Below, you can see two pictures of the same matrix with the rows and columns highlighted.

The dimensions of this matrix
• dimensions: 2 × 3
• 2 rows × 3 columns

### Matrix Notation

In order to identify an entry in a matrix, we simply write a subscript of the respective entry's row followed by the column.

In matrix A on the left, we write a23 to denote the entry in the second row and the third column.

One way to remember that this notation puts rows first and columns second is to think of it like reading a book. You always read sideways first, just as you always write the rows first. To continue the analogy, when you are done reading a row in a book, your eyes move downward, just as the columns after the rows.    A23 indicates the row number first, 2, then the column number 3.

### Practice Identifying Entries

Step 1

What are the dimensions of the matrix below?

The dimensions of the matrix are 3 × 3 (3 rows × 3 columns)

Step 2

Identify entry G23 in the matrix G on the left.

G23 is the entry in the second row and third column: 55.

Step 3

What are the dimensions of J?

The dimensions are 3 × 5 (3 rows × 5 columns)

Step 1

Identify entry j34

Entry j34 is the entry in the third row and fourth column.

Step 2

Identify entry J 12

J12 is the number in the first row and the second column: -5

Step 1

What are the dimensions of V below?

The dimensions of the matrix are 4 × 5 (4 rows × 5 columns)

Step 2

Identify entry v14

The entry is 31, (row 1 & column 4)

Step 3

What is the matrix notation to denote the entry in the bottom right corner, 15?

v45 denotes the entry in the fourth row and fifth column, the number 15 in the bottom right corner.