Left| {,begin{array}{*{20}{c}}{b + c}& a& ab& {c + a}& bc& c& {a + b}end{arr

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3 and 4 .Determinants and Matrices

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$\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

$3abc$

D

$4abc$

Solution

(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})\} $

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

Standard 12

Mathematics

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