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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants2 Marks
Question
Show that:$
\left|\begin{array}{ccc}
1 & a & b \\
-a & 1 & c \\
-b & -c & 1
\end{array}\right|=1+a^2+b^2+c^2
$
✓

Answer

On expanding along $R _1$$
\begin{array}{l}
=1\left(1+c^2\right)-a(-a+b c)+b(a c+b) \\
=1+c^2+a^2-a b c+a b c+b^2 \\
=1+a^2+b^2+c^2
\end{array}
$
Hence proved.

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