# Column Matrix

A Column Matrix is a matrix having only one column. The order of the column matrix is given by $$m \times 1$$, here, $$m$$ is the number of rows, arranged in a way that they represent a column of elements.

Rows and Columns in a matrix holds the elements. The row elements are arranged horizontally and the column elements are arranged vertically. Column matrices have a rectangular array of elements in a vertical line arrangement.

Index

## Column Matrices Representation

The column matrices are represented by:

$$A = \begin{bmatrix} a_{11}\\ a_{21}\\ …\\ a_{m1}\\ \end{bmatrix} _{m \times 1}$$

The determinant of column matrices is given only if the order is $$1 \times 1$$.

If the order of the matrix is $$m \times 1$$, where $$m > 1$$, then the determinant is undefined. Determinants are only defined for square matrices.

## Types of Matrices

There are different types of matrices, which are given below.

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

## Examples

$$A = \begin{bmatrix} 7\\ \end{bmatrix} _{1 x 1}$$

This a 1 X 1 matrix and has a single element.

$$B = \begin{bmatrix} 7\\ 8\\ 9\\ \end{bmatrix} _{3 x 1}$$

This a 3 X 1 matrix. Having 3 elements in 3 rows and 1 column.

## Questions

Question 1. What is [0] matrix?

Solution. [0] matrix can also be called as a null matrix.

Question 2. What is the order of given matrix.

$$\begin{bmatrix} 7 \\ 15 \\ 2 \\ 1 \\ \end{bmatrix}$$

Solution. The order of given matrix is 4 X 1.

## FAQs

What is a column matrix?

It is a matrix having only one column with order given by m x 1, where m is the number of rows, arranged in a way that they represent a column of elements.

What is the order of a column matrix?

Its order is given by m x 1.

How many columns are there in a column matrix?

There is only 1 column in column matrices but multiple rows.

What is the difference between column matrix and row matrix?

In column matrices, there is only 1 column and in row matrices, there will be only 1 row.

Related:

1. Singular Matrices

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