## What is a matrix?

A matrix is simply a table of numbers enclosed by a set of square brackets. These numbers may correspond to inventory levels, production quotas, or almost anything. We specify the size of a matrix by giving the number of rows and columns in the matrix.

An *m* x *n* matrix (read m by n) is a table of numbers with m rows and n columns enclosed by a set of square brackets.

The plural of matrix is matrices. The size of a matrix is always listed as row by column. Shown below are several matrices of various sizes.

Any matrix with only one row is also called a row matrix. The matrix in the center is an example of a row matrix. A matrix with only one column is called a column matrix. The matrix on the far right is an example of a column matrix.

Capital letters are used to name matrices. For instance, we might name the 3 x 2 matrix given above with the letter *A*,

The individual entries in the matrix are denoted by the corresponding lower case letter with a subscript. The number 4 in the third row and first column is called *a*_{31} and the number -1 in the second row and second column is called *a*_{22}. In fact, we can match any entry to its name using the lowercase letter matching its name with a subscript. In general, *a*_{mn} is the entry in the *m*^{th} row and *n*^{th} column.

### Example 1 Find the Matrix Entry

For the matrices

find the entries indicated in each part.

a. *b*_{12}

**Solution** Let’s examine the matrix entry in detail.

The entry in the first row and second column of the matrix **B** is 0.75.

b. *c*_{21}

**Solution** The entry in the second row and first column of C is 3.

c. *b*_{31}

**Solution** This entry matches with the number in the third row and second column of B. Since B only has two rows, does not exist for the given matrix B.