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
What are the dimensions of the matrix below? Dimensions
The dimensions of this matrix are
3 × 3 (3 rows × 3 columns)
Identify entry G23 in the matrix G on the left.
G23 is the entry in the second row and third column: 55.
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 correspondingentries (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.