If A= [ array ccc & & 0 - & & 0 0 & 0 & 1 array ] , where A₂₁, A₂₂, A₂₃ are cofactors of a₂₁, a₂₂, a₂₃ respectively, then the value of a₂₁ A₂₁+a₂₂ A₂₂+a₂₃ A₂₃=

Step-by-step solution

The expression a₂₁ A₂₁+a₂₂ A₂₂+a₂₃ A₂₃ represents the determinant expansion along the second row of matrix A . A= [ array ccc & & 0 - & & 0 0 & 0 & 1 array ] Expanding along the third column yields |A| = 0 A₁₃ + 0 A₂₃ + 1 A₃₃ = A₃₃ . The corresponding minor is M₃₃ = vmatrix & - & vmatrix = ^2 + ^2 = 1 , so A₃₃ = 1 . The determinant equals 1 , matching the original expression. Answer: A