- Home
- Standard 12
- Mathematics
3 and 4 .Determinants and Matrices
medium
$\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