Manipal MET2011MathematicsDeterminants
The value of | array ccc a^2 & b^2 & c^2 (a+1)^2 & (b+1)^2 & (c+1)^2 (a-1)^2 & (b-1)^2 & (c-1)^2 array | is
Options
- A3 | array lll a^2 & b^2 & c^2 a & b & c 1 & 1 & 1 array |
- B4 | array lll a^2 & b^2 & c^2 a & b & c 1 & 1 & 1 array |
- C2 | array lll a^2 & b^2 & c^2 a & b & c 1 & 1 & 1 array |
- DNone of these
Correct answer
B. 4 | array lll a^2 & b^2 & c^2 a & b & c 1 & 1 & 1 array |
Step-by-step solution
Let = | array ccc a^2 & b^2 & c^2 (a+1)^2 & (b+1)^2 & (c+1)^2 (a-1)^2 & (b-1)^2 & (c-1)^2 array | Applying R₂ R₂-R₃=4 | array ccc a^2 & b^2 & c^2 a & b & c (a-1)^2 & (b-1)^2 & (c-1)^2 array | Applying R₃ R₃- (R₁-2 R₂ )=4 | array ccc a^2 & b^2 & c^2 a & b & c 1 & 1 & 1 array |