Question

Find the determinant of the matrix: \[ \left| \begin{matrix} 21 & 11 & 10 \\ 25 & 15 & 10 \\ 64 & 27 & 37 \end{matrix} \right| \]

• A. 1190
• B. 841
• C. 0
• D. 1

Hint:

To calculate the determinant of a 3x3 matrix, use the standard formula involving cofactor expansion along the first row.

Answer 1

The Correct Option is C

We are given the matrix: \[ \left| \begin{matrix} 21 & 11 & 10 \\ 25 & 15 & 10 \\ 64 & 27 & 37 \end{matrix} \right| \] To find the determinant of a 3x3 matrix, we use the formula: \[ \text{det} \left( A \right) = a(ei - fh) - b(di - fg) + c(dh - eg) \] For the given matrix: \[ \left| \begin{matrix} 21 & 11 & 10 \\ 25 & 15 & 10 \\ 64 & 27 & 37 \end{matrix} \right| \] The determinant calculation becomes: \[ = 21 \left( (15 \times 37) - (10 \times 27) \right) - 11 \left( (25 \times 37) - (10 \times 64) \right) + 10 \left( (25 \times 27) - (15 \times 64) \right) \] After performing the multiplication and subtraction, we find that the determinant is \( 0 \). Thus, the correct answer is 0.