Column Matrix

A column matrix is a type of matrix that has only one column. The order of the column matrix is represented by m x 1, thus the rows will have single elements, arranged in a way that they represent a column of elements. On the other hand, unlike column matrix, a row matrix will have a single row only. Learn to determine the order of matrices at BYJU’S.

[aij]m x 1 is a column matrix

The determinant of a column matrix can be determined only if its order is 1 x 1. But if the order of the matrix is m x 1, where m is greater than 1 ,then the determinant is undefined. Therefore, determinants are only defined for square matrices. Let us understand more about the column matrix with examples. But before we go ahead with the column matrix, let us see how many times the matrices are there.

Types of Matrices

There are different types of matrices, in Maths.

1. Column matrix
2. Row matrix
3. Square matrix
4. Diagonal matrix
5. Scalar matrix
6. Identity matrix
7. Zero matrix

Definition of Column Matrix

Suppose, a matrix, m x n, where m represents the number of rows and n represents the number of columns, and n = 1, then the matrix is called the column matrix. Thus, the vertical lines of elements form a column matrix.

A column matrix is a rectangular array of elements, arranged in a vertical line. The general representation of the column matrix is given by:

$$Column~ Matrix, A =\left[\begin{array}{c} a_{11} \\ a_{21} \\ a_{31} \\ \vdots \\ a_{m 1} \end{array}\right]_{m \times 1}$$

Let us see some examples of column matrices.

Examples of Column Matrix

Example 1: An example of a column matrix of the order 1 x 1, is:

A = [3]

Here, there is only one element within the matrix, arranged in one row and one column. The determinant of this matrix is 3 (since it is also a square matrix).

Example 2: An example of a column matrix of the order 2 x 1, is:

$$A =\left[\begin{array}{c} 1 \\ 7 \end{array}\right]_{2 \times 1}$$

Here, there are two elements, arranged within the matrix, in two rows and one column.

Example 3: An example of a column matrix of the order 3 x 1, is:

$$A =\left[\begin{array}{c} 2 \\ 7 \\ 9 \end{array}\right]_{3 \times 1}$$

Here, there are three elements, arranged within the matrix, in three rows and one column.

Example 4: An example of a column matrix of the order 4 x 1, is:

$$A =\left[\begin{array}{c} 3 \\ 2 \\ 8 \\ 5 \end{array}\right]_{4 \times 1}$$

Here, there are three elements, arranged within the matrix, in four rows and one column.

Example 5: An example of a column matrix of the order 5 x 1, is:

$$A =\left[\begin{array}{c} 1 \\ 2 \\ 3 \\ 4 \\ 6 \end{array}\right]_{5 \times 1}$$

Here, there are three elements, arranged within the matrix, in five rows and one column.

In all the above examples, the elements are arranged in a single column, therefore, all these are column matrices.

Practice Questions

1. Give the examples of column matrix of the orders of:
1. 2 x 1
2. 3 x 1
3. 4 x 1
4. 5 x 1
5. 6 x 1
2. What is the order of the given matrix?
$$A =\left[\begin{array}{c} 4 \\ 0 \\ 1 \\ 3 \\ 8 \end{array}\right]$$

Frequently Asked Questions on Column Matrix

What is a column matrix?

A matrix is called a column matrix, if it has only one column. It is represented by Amx1, where m is the number of rows.

What is a column in a matrix?

The arrangement of elements in a single column represents the column matrix. A matrix is denoted by [aij]mxn, where i and j represent the position of elements in the matrix, row-wise and column-wise, m is the number of rows and n is the number of columns.

What is the order of the column matrix?

The order of the column matrix is m x 1, where m is the number of rows.

What is the difference between column matrix and row matrix?

A column matrix has a single column and a row matrix has a single row in the matrix.

Is [0] a column matrix?

[0] is a null matrix that can be a column matrix or a row matrix.

Give an example of a column matrix with order 1 x 1.

[5]1×1 is an example of a column matrix with order 1 x 1.