99 Percentile Qs Bank for JEE MainMathematicsDeterminants
| array ccc a-b-c & 2 a & 2 a 2 b & b-c-a & 2 b 2 c & 2 c & c-a-b array | is equal to
Options
- A0
- Ba+b+c
- C(a+b+c)^2
- D(a+b+c)^3
Correct answer
D. (a+b+c)^3
Step-by-step solution
Let = [ array ccc a-b-c & 2 a & 2 a 2 b & b-c-a & 2 b 2 c & 2 c & c-a-b array ] Applying R₁ R₁+R₂+R₃ and taking common (a+b+c) from R₁ =(a+b+c) | array ccc 1 & 1 & 1 2 b & b-c-a & 2 b 2 c & 2 c & c-a-b array | Applying C₂ C₂-C₁ and C₃ C₃-C₁ , aligned & =(a+b+c) | array ccc 1 & 0 & 0 2 b & -b-c-a & 0 2 c & 0 & -a-b-c array | & =(a+b+c)[(-b-c-a)(-a-b-c)] & =(a+b+c)^3 aligned