Explain each of the following and give an example in each: 1. Rectangular matrix ? 2. Row matrix? 3. Column matrix? 4. Identity matrix?

1. Rectangular matrix: A rectangular matrix is a matrix in which the number of rows is not equal to the number of columns. It can have any number of rows and columns.

Example:
\[ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \]

2. Row matrix: A row matrix is a matrix that has only one row and multiple columns.

Example:
\[ \begin{bmatrix} 1 & 2 & 3 \end{bmatrix} \]

3. Column matrix: A column matrix is a matrix that has only one column and multiple rows.

Example:
\[ \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \]

4. Identity matrix: An identity matrix is a square matrix in which all the elements of the main diagonal are 1 and all other elements are 0.

Example:
\[ \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \]

1. Rectangular Matrix:
A rectangular matrix is a matrix with m rows and n columns, denoted as m x n matrix. Each element in the matrix has a position (i, j), where i is the row index and j is the column index.

Example:
```
A = [1 2 3]
[4 5 6]
[7 8 9]
```
This is a 3 x 3 rectangular matrix.

2. Row Matrix:
A row matrix is a matrix with only one row and an arbitrary number of columns. It can be considered a special case of a rectangular matrix with m = 1.

Example:
```
B = [1 2 3 4 5]
```
This is a 1 x 5 row matrix.

3. Column Matrix:
A column matrix is a matrix with only one column and an arbitrary number of rows. It can be considered a special case of a rectangular matrix with n = 1.

Example:
```
C = [1]
[2]
[3]
[4]
[5]
```
This is a 5 x 1 column matrix.

4. Identity Matrix:
An identity matrix is a square matrix (m = n) where all the diagonal elements are 1, and all other elements are 0. It is denoted as I.

Example:
```
I = [1 0 0]
[0 1 0]
[0 0 1]
```
This is a 3 x 3 identity matrix.