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Determinants (p-1) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Determinants (p-1)1 Mark
Question
Without expanding, evaluate the following determinants.

(iii) $\left|\begin{array}{lll}2 & 7 & 65 \\ 3 & 8 & 75 \\ 5 & 9 & 86\end{array}\right|$

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Answer

Let $D=\left|\begin{array}{lll}2 & 7 & 65 \\ 3 & 8 & 75 \\ 5 & 9 & 86\end{array}\right|$
Applying $C_3 \rightarrow C_3-9 C_2$, we get
$
\begin{array}{rlrl}
\mathrm{D} & =\left|\begin{array}{lll}
2 & 7 & 2 \\
3 & 8 & 3 \\
5 & 9 & 5
\end{array}\right| & \text { MaharashtraBoardSolutions.in } \\
& =0 & & \ldots\left[\because C_1 \text { and } C_3 \text { are identical }\right]
\end{array}
$

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