Matrices & Determinants
Properties of determinants
Grade None
Question:
<p>If \Delta = \[ \begin{vmatrix} a1 & b1 & c1 \\ & a2 & b2 & c2 \\ & a3 & b3 & c3 \end{vmatrix} \] and A2, B2, C2 are cofactors of second row, then a1A2 + b1B2 + c1C2 equals:</p>
Step-by-Step Solution
Key Concept: Row \times cofactors of another row = 0 (orthogonality property).
1. **Identify pattern**: Row 1 elements with row 2 cofactors
2. **Apply property**: Different row \to sum = 0
3. **Final answer**: 0
Correct Answer: 2