If A= [ array ccc 1 & 1 & 1 2 & 1 & -3 -1 & 2 & 3 array ] , then A₃₁+A₃₂+A₃₃= where A_ i j , where A= [a_ i j ]_ 3 3

Step-by-step solution

We know that sum of the product of elements of one row of a determinant and cofactor of corresponding element of any other row is zero. aligned & a₁₁ A₃₁+a₁₂ A₃₂+a₁₃ A₃₃=0 & 1 A₃₁+1 A₃₂+1 A₃₃=0 A₃₁+A₃₂+A₃₃=0 aligned