Using the cofactors of the elements of the second column, evaluate Δ = |2, −1, 3; 1, 0, 4; −2, 5, 1|.

1. 1 · Write what is given and what is to be found. Given: Δ. To find: Δ using the cofactors of column 2, whose elements are −1, 0 and 5.
2. 2 · Write the rule. Δ = a₁₂A₁₂ + a₂₂A₂₂ + a₃₂A₃₂, with Aᵢⱼ = (−1)ⁱ⁺ʲ Mᵢⱼ.
3. 3 · Find the three cofactors.
   • A₁₂ = −|1, 4; −2, 1| = −(1 + 8) = −9
   • A₂₂ = +|2, 3; −2, 1| = 2 + 6 = 8
   • A₃₂ = −|2, 3; 1, 4| = −(8 − 3) = −5
4. 4 · Multiply and add. Δ = (−1)(−9) + 0 × 8 + 5 × (−5) = 9 + 0 − 25 = −16.
5. 5 · Check and box the answer. Along row 1: 2(0 − 20) + 1(1 + 8) + 3(5 − 0) = −40 + 9 + 15 = −16. Answer: Δ = −16.

Scoring tip: Write each cofactor with its sign in brackets first. A cofactor written without its sign is the most common slip.