# Define Row and Column Matrix with Examples

## What is Row Matrix?

A Matrix, which has only one row is called Row Matrix. i.e.,1×n matrix of the form a_ia_{i_2}a_{i_3}...a_{in} is said to be a row matrix. A row matrix is also called row vector.

### Example of Row Matrix

A=\begin{bmatrix}1&2&1&0\end{bmatrix}
The order of the above matrix is 1 × 4 because it contain 1 Row and 4 Columns.

It is most common example of row matrix because it contains only one row. There is no limit for row matrix that it could contain only few elements or members.

.i.e., A=\begin{bmatrix}1&2&0&1&…&n\end{bmatrix}

it is most satisfying example to prove that a Row Matrix could contain more elements. Its order is 1× n. Because it contain 1 Row and n Columns.

### Common Examples of Row Matrix

Some common examples of Row Matrix are as follows;

• A=\begin{bmatrix}1&2\end{bmatrix}
• B=\begin{bmatrix}1&2&3\end{bmatrix}
• C=\begin{bmatrix}1&0&2&0\end{bmatrix}

#### Transpose of Row Matrix

Transpose of a row matrix is obtained by interchanging rows into columns and columns into rows.

#### Rank of a Row Matrix

Let A be a non zero matric. If r is the number of non zero rows then it is reduced to reduced echelon form , then r us called the (row) rank of the matrix A. In simple words Number of non zero rows in a matrix is called Rank. It is obtained by applying row operation.

## what is Column Matrix?

A Matrix which has only one column is called Column matrix. , i.e., m×1 matrix of the form
A=\begin{bmatrix}1\\2\\3\end{bmatrix} is said to be a Column Matrix or column vector.

#### Examples of Column Matrix

• A=\begin{bmatrix}1\\2\end{bmatrix}
• B=\begin{bmatrix}1\\2\\0\end{bmatrix}
• C=\begin{bmatrix}1\\2\\3\\4\end{bmatrix}

#### Transpose of Column Matrix

Transpose of columns matrix is also as similar as Row matrix. It is also obtained by changing the order m×n into n×m.

#### Difference between Row Matrix and Column Matrix

Main difference between Row and Column matrix it that Row matrix contain single row and Column matrix contain single column.

Addition of a matrix is only possible when order of both matrix is equal. It means that number of rows and number of columns should be equal. It is obtained by adding each entry of A to corresponding entry of B.

##### Row and column matrix in the case of Determinant

(i) If two rows in a matrix are identical or two columns are identical(means if these are totally same), their determinant would be zero. It means \left|A\right|=0.

##### “Elementary Row and Column Operation of Matrix“

Usually a given system of linear equation is reduced to a simple equivalent system by applying in turn finite number of elementary operations which are:

• Interchanging two equations
• Multiplying an equation by a non zero number
• Adding a multiple of one equation to another equation.
###### Corresponding to these three elementary operations, the following elementary operations are applied to matrices to obtain equivalent matrices:
• Interchanging two rows.
• Multiplying a row by a non zero number.
• Adding a multiple of one row to another row.

#### EXAMPLE OF ROW OPERATION IS:R2 –> R2

Now we state that elementary column operations are:

• Interchanging two columns.
• Multiplying a column by a non zero number.
• Adding a multiple of one column to another column.

Marices A and B are equivalent if B can be obtained by applying in turn a finite number of row operations on A.