In a 3 × 3 determinant, the elements of row 1 are 2, $-1$ and 3, and their cofactors are 4, 5 and $-2$. What is the value of the determinant?

Explanation

1. 01

   $\Delta = a_{11}A_{11} + a_{12}A_{12} + a_{13}A_{13}$, and the cofactors already carry their signs.

2. 02

   $2(4) + (-1)(5) + 3(-2) = 8 - 5 - 6 = -3$.