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Determinants and Matrices — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDeterminants and Matrices2 Marks
Question
Without expanding, evaluate the following determinants :

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

✓

Answer

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

Taking $(3 x)$ common from $R_3$, we get

$D=3 x\left|\begin{array}{ccc}2 & 3 & 4 \\ 5 & 6 & 8 \\ 2 & 3 & 4\end{array}\right|$

= (3x)(0) = 0

$\ldots\left[\because R_1\right.$ and $R_3$ are identical $]$

= 0

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