AP EAMCET202421 May 2024Evening ShiftMathematicsDeterminantsActual
| array ccc a+b+2 c & a & b c & b+c+2 a & b c & a & c+a+2 b array |=
Options
- A(a+b+c)^3
- B2(a+b+c)^3
- C3(a+b+c)^3
- D(a+b+c)
Correct answer
B. 2(a+b+c)^3
Step-by-step solution
= | array ccc a+b+2 c & a & b c & b+c+2 a & b c & a & c+a+2 b array | Applying, C₁ C₁+C₂+C₃ , we get =2(a+b+c) | array ccc 1 & a & b 1 & 2 a+b+c & b 1 & a & a+2 b+c array | Applying, R₂ R₂-R₁ ; R₃ R₃-R₁ aligned & =2(a+b+c) | array ccc 1 & a & b 0 & a+b+c & 0 0 & 0 & a+b+c array | & =2(a+b+c)^3 . aligned