NCERT Class 12 · Ch 4 Exercise 4.3 · Q5
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.3 Question 5
For A=[aᵢⱼ] of order 3, with Aᵢⱼ denoting cofactors, which expression equals det A?
💡 Concept Hints
- Identify whether this needs determinant expansion, an inverse, or the absolute determinant formula for area.
- For a determinant use signed cofactors. For a system first check invertibility; for an area take half the absolute determinant.
✅ Step-by-Step Solution
Final Answer: D: a₁₁A₁₁+a₂₁A₂₁+a₃₁A₃₁.
- Laplace expansion pairs every element of a chosen row or column with its own cofactor.
- Option D uses all three entries of column 1 with those same-index cofactors. It is the valid column expansion.
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