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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
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
  • A
    $a + b + c$
  • B
    ${(a + b + c)^2}$
  • ✓
    $0$
  • D
    $1 + a + b + c$
✓

Answer

Correct option: C.
$0$
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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