The value of the determinant | , * 20 c 1&a& b + c 1&b& c + a 1&c… - Vidyadip

Question

The value of the determinant $\left| {\,\begin{array}{*{20}{c}}1&a&{b + c}\\1&b&{c + a}\\1&c&{a + b}\end{array}\,} \right|$is

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Answer

c
(c) $\Delta = \left| {\,\begin{array}{*{20}{c}}1&a&{b + c}\\1&b&{c + a}\\1&c&{a + b}\end{array}\,} \right| = (a + b + c)\,\left| {\,\begin{array}{*{20}{c}}1&1&{b + c}\\1&1&{c + a}\\1&1&{a + b}\end{array}\,} \right|$
$({C_2} \to {C_2} + {C_3})= 0$,

$(\because \,\,{{C}_{1}}\equiv {{C}_{2}})$

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