The trace of the matrix A `[(2,5,9),(7,-5,3),(2,6,8)]` is equal to

Options

A. 6
B. 5
C. 3
D. None of these

Answer

To find the trace of the matrix \( A = \begin{pmatrix} 2 & 5 & 9 \\ 7 & -5 & 3 \\ 2 & 6 & 8 \end{pmatrix} \), we need to sum the diagonal elements of the matrix. The diagonal elements are the elements that run from the top left corner to the bottom right corner of the matrix.

### Step-by-Step Solution:

1. **Identify the diagonal elements**:
The diagonal elements of the matrix \( A \) are:
- First diagonal element (top left): \( 2 \)
- Second diagonal element (middle): \( -5 \)
- Third diagonal element (bottom right): \( 8 \)

2. **Sum the diagonal elements**:
Now, we will sum these diagonal elements:
\[ \text{Trace}(A) = 2 + (-5) + 8 \]

3. **Calculate the sum**:
- First, calculate \( 2 + (-5) = 2 - 5 = -3 \)
- Now, add \( -3 + 8 = 5 \)

4. **Final result**:
Therefore, the trace of the matrix \( A \) is:
\[ \text{Trace}(A) = 5 \]

### Final Answer:
The trace of the matrix \( A \) is \( 5 \).