If A= [ array ccc x & 1 & 2 2 & 4 & x -3 & 3 & 2 array ] is a singular matrix and the distinct values of x are x₁ and x₂ , then x₁+x₂+x₁ x₂= .

Step-by-step solution

Given, A= [ array ccc x & 1 & 2 2 & 4 & x -3 & 3 & 2 array ] is singular, when aligned & | array lll A =0 x & 1 & 2 2 & 4 & x -3 & 3 & 2 array |=0 & x(8-3 x)-1(4+3 x)+2(6+12)=0 & 8 x-3 x^2-4-3 x+36=0 & 3 x^2-5 x-32=0 & x₁+x₂= 5 3 and x₁ x₂=- 32 3 & x₁+x₂+x₁ x₂= 5 3 - 32 3 =- 27 3 =-9 aligned