Question

If `Delta=|[a_(11),a_(12),a_(13)],[a_(21),a_(22),a_(23)],[a_(31),a_(32),a_(33)]|` and `A_(i j)` is cofactors of `a_(i j)`, then value of `Delta` is given by
A. `a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)`
B. `a_(11)A_(11)+a_(12)A_(21)+a_(13)A_(31)`
C. `a_(21)A_(11) + a_(22)A_(12) + a_(23)A_(13)`
D. `a_(11)A_(11) + a_(21)A_(21) + a_(31)A_(31)`

Answer 1

We know, value of a determinant can be evaluated by multiplying the same element of matrix with the corresponding cofactors.
`:. Delta = sum (A_(ij)) (a_(ij))`
In other words, `ij` should be same for both `a` and `A`.
In the given options, only option `D` satisfies this condition.
`:. Delta = a_11A_11+a_21A_21+a_31A_31`