AP EAMCET202119 Aug 2021Evening ShiftMathematicsDeterminantsActual
The value of b + c a a b c + a b c c a + b is
Options
- Aa b c
- B( a + b ) ( b + c ) ( c + a )
- C4 a b c
- D( a − b ) ( b − c ) ( c − a )
Correct answer
C. 4 a b c
Step-by-step solution
Let △ = b + c a a b c + a b c c a + b . Applying R 1 → R 1 + R 2 + R 3 △ = b + c + b + c a + c + a + c a + b + a + b b c + a b c c a + b ⇒ △ = 2 b + c 2 a + c 2 a + b b c + a b c c a + b ⇒ △ = 2 b + c a + c a + b b c + a b c c a + b Applying R 1 → R 1 - R 2 ⇒ △ = 2 b + c - b a + c - ( c + a ) a + b - b b c + a b c c a + b ⇒ △ = 2 c 0 a b c + a b c c a + b Applying R 3 → R 3 - R 1 ⇒ △ = 2 c 0 a b c + a b 0 c b Applying R 2 U