Lesson Objectives

- Learn how to determine the dimensions of a matrix

## How to Find the Order of a Matrix

In this lesson, we want to learn how to find the order or dimensions of a matrix. When we talk about a matrix, normally, we are speaking about an ordered array or we could say a rectangular array of numbers. The numbers inside of a matrix are called elements or sometimes entries of the matrix. The entries for a matrix may also include symbols or expressions. $$\left[ \begin{array}{cc}a&b\\ c&d\end{array}\right] $$

Example #1: Find the order of the matrix. $$\left[ \begin{array}{ccc}5&2&1\\ -4&7&6\end{array}\right] $$ This matrix is a 2 x 3 matrix. It has 2 rows and 3 columns.

Example #2: Find the order of the matrix. $$\left[ \begin{array}{cccc}6&-2&4&1\\ 9&8&4&-3\\ 1&14&5&6\end{array}\right] $$ This matrix is a 3 x 4 matrix. It has 3 rows and 4 columns.

### The Order of a Matrix

The order or dimensions of a matrix are given as the number of rows by the number of columns. When we think of rows, we are thinking about the horizontal entries. When we think about the columns, we are thinking about the vertical entries.Example #1: Find the order of the matrix. $$\left[ \begin{array}{ccc}5&2&1\\ -4&7&6\end{array}\right] $$ This matrix is a 2 x 3 matrix. It has 2 rows and 3 columns.

Example #2: Find the order of the matrix. $$\left[ \begin{array}{cccc}6&-2&4&1\\ 9&8&4&-3\\ 1&14&5&6\end{array}\right] $$ This matrix is a 3 x 4 matrix. It has 3 rows and 4 columns.

#### Skills Check:

Example #1

Find the order of the matrix. $$\left[ \begin{array}{ccc}3&9&2\\ 5&6&4 \\2& 1& 9\end{array}\right] $$

Please choose the best answer.

A

9 x 3

B

3 x 6

C

3 x 5

D

4 x 3

E

3 x 3

Example #2

Find the order of the matrix. $$\left[ \begin{array}{ccc}5&2&1&7\\ -4&7&6&10\end{array}\right] $$

Please choose the best answer.

A

2 x 4

B

4 x 2

C

8 x 4

D

6 x 3

E

2 x 2

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