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Determinants — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDeterminants1 Mark
Question
$\left|\begin{array}{ccc}-a & b & c \\ a & -b & c \\ a & b & -c\end{array}\right|=k a b c$, then the value of $k$ is:
✓

Answer

We have,
$\begin{aligned}
\left|\begin{array}{ccc}
-a & b & c \\
a & -b & c \\
a & b & -c
\end{array}\right| & =-a(b c-b c)-b(-a c-a c)+c(a b+a b) \\
& =2 a b c+2 a b c=4 a b c
\end{aligned}$
$\Rightarrow k a b c=4 a b c \Rightarrow k=4$

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