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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.

(ii) $\left|\begin{array}{ccc}2 & 3 & 4 \\ 5 & 6 & 8 \\ 6 x & 9 x & 12 x\end{array}\right|$

✓

Answer

Let $\mathrm{D}=\left|\begin{array}{ccc}2 & 3 & 4 \\ 5 & 6 & 8 \\ 6 x & 9 x & 12 x\end{array}\right|$
Taking ( $3 x$ ) common from $\mathrm{R}_3$, we get
$
\begin{aligned}
& \mathrm{D}=3 x\left|\begin{array}{lll}
2 & 3 & 4 \\
5 & 6 & 8 \\
2 & 3 & 4
\end{array}\right| \\
& \text { MaharashtraBoardSolutions.in } \\
&=(3 x)(0) \quad \ldots\left[\because \mathrm{R}_1 \text { and } \mathrm{R}_3 \text { are identical }\right] \\
&=0
\end{aligned}
$

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