Question

Let A = \(\begin{bmatrix} \log_5 128 & \log_4 5  \log_5 8 & \log_4 25 \end{bmatrix}\) \). If \(A_{ij}\)  is the cofactor of \( a_{ij} \), \( C_{ij} = \sum_{k=1}^2 a_{ik} A_{jk} \), and \( C = [C_{ij}] \), then \( 8|C| \) is equal to:

• A. 242
• B. 222
• C. 262
• D. 288

Hint:

To calculate the determinant of a matrix with cofactors, use the cofactor expansion method and simplify the resulting expression.

Answer 1

The Correct Option is C

To find \( 8|C| \), we first need to calculate the determinant of the matrix \( A \). After calculating the cofactors and the determinant of \( C \), we find that \( 8|C| = 262 \).