Question

If \[ A = \begin{pmatrix} 1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9 \end{pmatrix}, \] then the trace of matrix \( A \) is:

• A. 17
• B. 25
• C. 3
• D. 12

Hint:

The trace of a matrix is the sum of its diagonal elements. For a 3x3 matrix, simply add the elements from the top left to the bottom right diagonal.

Answer 1

The Correct Option is A

The trace of a square matrix is the sum of the elements on the main diagonal (the diagonal from the top left to the bottom right). For the given matrix \( A \), the main diagonal elements are: \[ 1, 7, 9. \] So, the trace of matrix \( A \) is: \[ \text{Trace}(A) = 1 + 7 + 9 = 17. \]
Step 2: Conclusion.
Therefore, the trace of matrix \( A \) is \( 17 \), and the correct answer is (a).