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

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Determinants (p-1)2 Marks
Question
Without expanding determinants, find the value of

(ii) $\left|\begin{array}{lll}2014 & 2017 & 1 \\ 2020 & 2023 & 1 \\ 2023 & 2026 & 1\end{array}\right|$

✓

Answer

Let $\mathrm{D}=\left|\begin{array}{lll}2014 & 2017 & 1 \\ 2020 & 2023 & 1 \\ 2023 & 2026 & 1\end{array}\right|$
Applying $\mathrm{C}_2 \rightarrow \mathrm{C}_2-\mathrm{C}_1$, we get
$
D=\left|\begin{array}{lll}
2014 & 3 & 1 \\
2020 & 3 & 1 \\
2023 & 3 & 1
\end{array}\right|
$
Taking (3) common from $\mathrm{C}_2$, we get
$
\begin{aligned}
\mathrm{D} & =3\left|\begin{array}{lll}
2014 & 1 & 1 \\
2020 & 1 & 1 \\
2023 & 1 & 1
\end{array}\right| \text { } \\
& =3(0) \\
& =3
\end{aligned}
$

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