Class 12 Determinants · Short Answer2 Marksminors_and_cofactors
Class 12 Maths · Determinants · Short Answer #89
Expand using cofactors of the third column: \(\begin{vmatrix}1 & x & yz\\1 & y & zx\\1 & z & xy\end{vmatrix}\).
✅ Step-by-Step Solution
Final Answer: (x−y)(y−z)(z−x)
- The third-column cofactors are C₁₃=z−y,C₂₃=x−z,C₃₃=y−x.
- Expansion gives yz(z−y)+zx(x−z)+xy(y−x)=yz²−y²z+x²z−xz²+xy²−x²y.
- Factoring gives (x−y)(y−z)(z−x).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The third-column cofactors are C₁₃=z−y,C₂₃=x−z,C₃₃=y−x.
- [1 mark] Expansion gives yz(z−y)+zx(x−z)+xy(y−x)=yz²−y²z+x²z−xz²+xy²−x²y.
- [0.5 marks] Factoring gives (x−y)(y−z)(z−x).
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