The value of the determinant \(\begin{vmatrix}1 & 7 & 13\\ 1 & 9 & 11\\ 1 & 12 & 8\end{vmatrix}\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0
In every row the second and third entries add up to 20. Apply the column operation \(C_2 \to C_2 + C_3\):
\(\displaystyle \Delta = \begin{vmatrix}1 & 20 & 13\\ 1 & 20 & 11\\ 1 & 20 & 8\end{vmatrix}\)
Take 20 common from the second column:
\(\displaystyle \Delta = 20\begin{vmatrix}1 & 1 & 13\\ 1 & 1 & 11\\ 1 & 1 & 8\end{vmatrix}\)
Now the first two columns are identical, so the determinant is zero.
\(\Delta = 20 \times 0 = 0\)