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 Matri**ces** 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.

- Column Matrices
- Row Matrices
- Square Matrices
- Diagonal Matrices
- Scalar Matrices
- Identity Matrices
- 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.

**Question**s

**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.

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