Let =- 1 2 +i 3 2 , then value of the determinant = | array ccc 1 & 1 & 1 1 & -1- ^2 & ^2 1 & ^2 & array | is

Step-by-step solution

Applying R₂ R₂-R₁ ; R₃ R₃-R₁ , the given determinant becomes aligned & = | array ccc 1 & 1 & 1 0 & -2- ^2 & ^2-1 0 & ^2-1 & -1 array | & =1 [( -1) (-2- ^2 )- ( ^2-1 ) ( ^2-1 ) ] -1(0)+1(0) & = (-2- ^2 )( -1)- ( ^2-1 )^2 & =-2 +2- ^3+ ^2- ( ^4+1-2 ^2 ) & =-2 +1+ ^2- ( +1-2 ^2 ) & =3 ^2-3 & =3 ( -1) aligned