| , * 20 c b + c & a& a & c + a & b & c& a + b , | = - Vidyadip

MCQ

$\left| {\,\begin{array}{*{20}{c}}{b + c}& a& a\\b& {c + a}& b\\c& c& {a + b}\end{array}\,} \right| = $

A
$abc$
B
$2abc$
C
$3abc$
✓
$4abc$

✓

Answer

Correct option: D.

$4abc$

d
(d) $\left| {\,\begin{array}{*{20}{c}}{b + c}& a & a\\b& {c + a}& b\\c& c& {a + b}\end{array}\,} \right|\, $

$= \,\left| {\,\begin{array}{*{20}{c}}0& { - 2c}& { - 2b}\\b& {c + a}& b\\c& c& {a + b}\end{array}\,} \right|$

$\{$by ${R_1} \to {R_1} - ({R_2} + {R_3})\} $

$= 2c b(a + b - c)\, - 2b.c(b - c - a)\, = 4abc$

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