If `A=[a_(ij)]_(mxxn),B=[b_(ij)]_(mxxn)` then the element `C_(23)` of the matrix `C=A+B` is

Options

A. `a_(13)+b_(13)`
B. `a_(23)+b_(32)`
C. `a_(23)+b_(23)`
D. `a_(32)+b_(23)`

Answer

To find the element \( C_{23} \) of the matrix \( C \), where \( C = A + B \), we follow these steps:

### Step-by-Step Solution:

1. **Understand the Matrices**: We have two matrices \( A \) and \( B \), both of size \( m \times n \). The elements of these matrices are denoted as \( A = [a_{ij}] \) and \( B = [b_{ij}] \).

2. **Define the Resultant Matrix**: The resultant matrix \( C \) is defined as \( C = A + B \). This means that each element of matrix \( C \) is the sum of the corresponding elements of matrices \( A \) and \( B \).

3. **Identify the Element**: We need to find the specific element \( C_{23} \) in matrix \( C \). The notation \( C_{23} \) refers to the element in the second row and third column of matrix \( C \).

4. **Apply the Addition Rule**: According to the rules of matrix addition, the element \( C_{ij} \) is given by:
\[ C_{ij} = A_{ij} + B_{ij} \]
Therefore, for our specific case:
\[ C_{23} = A_{23} + B_{23} \]

5. **Conclusion**: Thus, the element \( C_{23} \) of the matrix \( C \) is:
\[ C_{23} = a_{23} + b_{23} \]

### Final Answer:
The element \( C_{23} \) of the matrix \( C \) is \( a_{23} + b_{23} \).

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