

Matrix NotationEntry, 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. This Page: matrix notation  adding & subtracting Related Matrix Pages: equality  matrix equations multiplying  directed graphs Scientific calculator with Matrix functions (mulitply, add , subtract matrices and more)
Example of a Matrix
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
dimensions: 2 × 3 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 a_{23} 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. A_{23} indicates the row number first, 2, then the column number 3.
Practice Identifying Entries
What are the dimensions of the matrix below?
Dimensions The dimensions of this matrix are 3 × 3 (3 rows × 3 columns) Identify entry G_{23} in the matrix G on the left. Entry G_{23} is the entry in the second row and third column: 55.
What are the dimensions of J ?
Dimensions The dimensions are 3 × 5 (3 rows × 5 columns) Identify entry j_{34} Answer Entry j_{34} is the entry in the third row and fourth column.
What are the dimensions of V below?
Answer
The dimensions of this matrix are 4 × 5 (4 rows × 5 columns) Identify entry v_{14} Answer The entry is 31, (row 1 & column 4)
What is the matrix notation to denote the entry in the bottom right corner, 15?
Answer
v_{45} denotes the entry in the fourth row and fifth column, the number 15 in the bottom right corner. 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. This Page: matrix notation  adding & subtracting Related Matrix Pages: equality  matrix equations multiplying  directed graphs matrix movie effect 