Often we can represent information in a rectangular group, like in the following table:
| Preferred colour | Female | Male |
|---|---|---|
| Black | $13$13 | $6$6 |
| Green | $3$3 | $10$10 |
| Purple | $8$8 | $9$9 |
This table of information can also be represented as a matrix. In mathematics, a matrix is a particular method of displaying information. It is any rectangular array of numbers, symbols, or expressions arranged in rows and columns. So the table above would be represented by a matrix, which we can call $A$A and is shown below.
We refer to the dimensions or order of a matrix as a reference to the number of rows and number of columns.
A matrix with dimensions $m\times n$m×n has $m$m rows and $n$n columns. For instance, the following matrix has dimensions $3\times4$3×4.
Elements are the individual entries of a matrix. An element can be identified by its position (that is, its row and column) in the matrix. For the following matrix $B$B, the element in the second row and third column is $7$7, where we use the following notation $b_{23}=7$b23=7.
Generally, we may represent any matrix as the following.
A matrix is a rectangular array of numbers, symbols or expressions.
The dimensions or order of a matrix is the number of rows and columns, denoted by $m\times n$m×n.
The elements of a matrix are the entries where $a_{ij}$aij denotes the element in the $i$ith row and $j$jth column of the matrix.
Practice questions
Question 1
| Determine the dimensions of the matrix | $-1$−1 | $-4$−4 | . | ||||
| $-9$−9 | $9$9 |
$\editable{}$$\times$×$\editable{}$
Question 2
| What is the entry at $a_{23}$a23 in $A$A$=$= |
|
? |
Types of matrices
A row matrix or row vector has just a single row. The following matrix $T$T is an example of a row matrix.
A column matrix or column vector has just a single column. The following matrix $M$M is an example of a column matrix.
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An identity matrix is a special type of diagonal matrix where all the elements on the main diagonal are ones.
For example: 
Matrix $N$N is also called a binary matrix as it consists entirely of $1$1's and $0$0's.
A zero matrix is a matrix of any dimension where all of the elements are zero. For example: 
Practice questions
Question 3
Identify the row matrix.
$4$4 $-4$−4 $-2$−2 $-1$−1 $0$0 $3$3 A$-4$−4 $1$1 $4$4 B$-3$−3 $5$5 $-4$−4 $-1$−1 C$3$3 $-2$−2 $2$2 D