NCERT Class 12 · Ch 4 Exercise 4.3 · Q3
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.3 Question 3
Evaluate \(\left[\begin{matrix}5 & 3 & 8\\2 & 0 & 1\\1 & 2 & 3\end{matrix}\right]\) by expanding along the second row.
💡 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: \(7\)
- Expand the determinant along row 2, using cofactors Cᵢⱼ=(−1)ⁱ⁺ʲMᵢⱼ.
- The cofactors in this row are \(\left[\begin{matrix}7 & 7 & -7\end{matrix}\right]\).
- The expansion terms are \(14\), \(0\), \(-7\).
- Adding and simplifying gives det A = \(7\).
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