Find minors and cofactors of the elements of the determinant`|[2,-3, 5],[6, 0, 4],[1, 5,-7]|`and verify that `a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)=0`

Explanation

To solve the problem, we need to find the minors and cofactors of the elements of the determinant \( | \begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix} | \) and verify that \( a_{11}A_{31} + a_{12}A_{32} + a_{13}A_{33} = 0 \).

### Step 1: Calculate the minors

1. **Minor \( M_{11} \)**:
- Remove the first row and first column:
\[
M_{11} = \begin{vmatrix} 0 & 4 \\ 5 & -7 \end{vmatrix} = (0 \cdot -7) - (4 \cdot 5) = 0 - 20 = -20
...