Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>Which relation is incorrect for determinant \Delta with cofactors?</p>
a1A1 + b1B1 + c1C1 = \Delta
a2A2 + b2B2 + c2C2 = \Delta
a3A3 + b3B3 + c3C3 = \Delta
a1A2 + b1B2 + c1C2 = \Delta
Step-by-Step Solution
Key Concept: Same row \times cofactors = \Delta, different row \times cofactors = 0.
1. **Check each option**
2. **Same row expansions** \to valid = \Delta
3. **Different row case (D)** \to equals 0
4. **Thus incorrect option = D
Correct Answer: 4