Manipal MET2018MathematicsDeterminants
The value of | array ccc a & a+b & a+2 b a+2 b & a & a+b a+b & a+2 b & a array | is equal to
Options
- A9 a^2(a+b)
- B9 b^2(a+b)
- Ca^2(a+b)
- Db^2(a+b)
Correct answer
B. 9 b^2(a+b)
Step-by-step solution
| array ccc a & a+b & a+2 b a+2 b & a & a+b a+b & a+2 b & a array | aligned & = | array ccc 3(a+b) & 3(a+b) & 3(a+b) a+2 b & a & a+b a+b & a+2 b & a array | (R₁ R₁+R₂+R₃ ) & =3(a+b) | array ccc 1 & 0 & 0 a+2 b & -2 b & -b a+2 b & b & -b array | C₂ C₂-C₁ C₃ C₃-C₁ & =3(a+b) | array cc -2 b & -b b & -b array | & =3 b^2(a+b) | array rr 2 & 1 -1 & 1 array |=3 b^2(a+b)(2+1)=9 b^2(a+b) aligned