The value of […] is

The correct answer is Option (3) → 0

The row operations \(R_1 \rightarrow R_1 - R_2\) and then \(R_2 \rightarrow R_2 - R_3\) do not change the determinant and make the numbers smaller:

    \(\displaystyle \Delta = \begin{vmatrix}25 & 15 & 21\\21 & 27 & 17\\219 & 198 & 181\end{vmatrix}\)

Expanding along the first row, the three minors are

    \(27 \times 181 - 17 \times 198 = 4887 - 3366 = 1521\)
    \(21 \times 181 - 17 \times 219 = 3801 - 3723 = 78\)
    \(21 \times 198 - 27 \times 219 = 4158 - 5913 = -1755\)

So

    \(\Delta = 25(1521) - 15(78) + 21(-1755)\)
    \(= 38025 - 1170 - 36855\)
    \(= 0\)