Definition and Examples of a Matrix, its entries, rows, columns, Matrix Notation. A Matrix is simply...

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.

This Page: matrix notation | adding & subtracting
Related Matrix Pages: equality | matrix equations |multiplying | directed graphs
matrix movie effect

Example of a Matrix

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!

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. example of matrix notation

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

What are the dimensions of the matrix below?
Dimensions

dimensions of matrix

Identify entry G₂₃ in the matrix G on the left.
Entry

What are the dimensions of J ?
Dimensions

Identify entry j₃₄ Answer

Identify entry J ₁₂ Answer

What are the dimensions of V below? Answer

dimensions of matrix

Identify entry v₁₄
Answer

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

Adding and Subtracting Matrices

You can add or subtract matrices if each matrix has the same dimensions (in other words, each one needs to have exactly the same number of columns and rows).

To add or subtract matrices , you just add or subtract the corresponding entries (the entries or numbers that are in the same spot).

Why are the same dimensions required for addition and subtraction?
Think about it: Since adding/subtracting matrices involves adding/subtracting corresponding entries.What would you do with the entries in the one matrix that do not have a corresponding entry in the other?)

Consider the example pictured on the left. Matrix #1 has an one more column than #2. How would you match, let alone add, the entries of #1's column 3 with corresponding ones in #2.

Matrix Notation

Entry, Rows and Columns

Matrix Notation

Adding and Subtracting Matrices