Question
Write the value of the determinant:
$\left|\begin{array}{ccc}102 & 18 & 36 \\1 & 3 & 4 \\17 & 3 & 6\end{array}\right|$
$\left|\begin{array}{ccc}102 & 18 & 36 \\1 & 3 & 4 \\17 & 3 & 6\end{array}\right|$
✓
Answer
Let, $\Delta=\left|\begin{array}{ccc}102 & 18 & 36 \\ 1 & 3 & 4 \\ 17 & 3 & 6\end{array}\right|$
$=\left|\begin{array}{ccc}17 & 3 & 6 \\ 1 & 3 & 4 \\ 17 & 3 & 6\end{array}\right| \quad\left[R_1 \rightarrow \frac{1}{6} R_1\right]$
$=0\quad \therefore (R_{1}$ and $R_{3}$ are identical$)$
$=\left|\begin{array}{ccc}17 & 3 & 6 \\ 1 & 3 & 4 \\ 17 & 3 & 6\end{array}\right| \quad\left[R_1 \rightarrow \frac{1}{6} R_1\right]$
$=0\quad \therefore (R_{1}$ and $R_{3}$ are identical$)$
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