NCERT Class 12 · Ch 4 Exercise 4.1 · Q6
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.1 Question 6
Evaluate the determinant of \(\left[\begin{matrix}1 & 1 & -2\\2 & 1 & -3\\5 & 4 & -9\end{matrix}\right]\).
💡 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: \(0\)
- Expand the determinant along row 1, using cofactors Cᵢⱼ=(−1)ⁱ⁺ʲMᵢⱼ.
- The cofactors in this row are \(\left[\begin{matrix}3 & 3 & 3\end{matrix}\right]\).
- The expansion terms are \(3\), \(3\), \(-6\).
- Adding and simplifying gives det A = \(0\).
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