AP EAMCET202120 Aug 2021Morning ShiftMathematicsDeterminantsActual
What is the value of a b c a - b b - c c - a b + c c + a a + b = ?
Options
- Aa 3 + b 3 + c 3 + 3 a b c
- Ba 3 + b 3 + c 3 - 3 a b c
- Ca 3 + b 3 + c 3 - 6 a b c
- Da 3 + b 3 + c 3 + 6 a b c
Correct answer
B. a 3 + b 3 + c 3 - 3 a b c
Step-by-step solution
a b c a - b b - c c - a b + c c + a a + b   ( R 2 → R 2 - R 1 ) = a b c - b - c - a b + c c + a a + b ( R 3 → R 3 + R 2 ) And taking out - 1 As common - 1 a b c b c a c a b Solving the determinant we get = - 1 [ a ( c b - a 2 ) - b ( b 2 - a c ) + c ( a b - c 2 ) ] = - 1 [ 3 a b c - a 3 - b 3 - c 3 ] = a 3 + b 3 + c 3 - 3 a b c