If number of elements is 20 then how many different types of matrices can be formed if number of rows is always even?

Options

A. 3
B. 4
C. 5
D. 6

Answer

To solve the problem of how many different types of matrices can be formed with 20 elements, given that the number of rows is always even, we can follow these steps:

### Step 1: Understand the relationship between rows, columns, and elements
The total number of elements in a matrix is given by the product of the number of rows (R) and the number of columns (C):
\[ R \times C = 20 \]

### Step 2: Identify the condition for rows
Since the number of rows (R) must always be even, we can list the possible even factors of 20. The even factors of 20 are:
- 2
- 4
- 10
- 20

### Step 3: Calculate the corresponding columns for each even row
Now, we will calculate the corresponding number of columns (C) for each even row (R):

1. **If R = 2**:
\[ C = \frac{20}{2} = 10 \]
(Matrix of size 2 x 10)

2. **If R = 4**:
\[ C = \frac{20}{4} = 5 \]
(Matrix of size 4 x 5)

3. **If R = 10**:
\[ C = \frac{20}{10} = 2 \]
(Matrix of size 10 x 2)

4. **If R = 20**:
\[ C = \frac{20}{20} = 1 \]
(Matrix of size 20 x 1)

### Step 4: List the possible matrices
From the calculations above, we have the following matrices:
1. 2 x 10
2. 4 x 5
3. 10 x 2
4. 20 x 1

### Step 5: Count the number of different matrices
We have found 4 different types of matrices that can be formed under the given conditions.

### Final Answer:
The number of different types of matrices that can be formed is **4**.

---