NCERT Class 12 · Ch 4 Exercise 4.4 · Q2
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.4 Question 2
Find the adjoint of \(\left[\begin{matrix}1 & -1 & 2\\2 & 3 & 5\\-2 & 0 & 1\end{matrix}\right]\).
💡 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: \(\left[\begin{matrix}3 & 1 & -11\\-12 & 5 & -1\\6 & 2 & 5\end{matrix}\right]\)
- Evaluate signed minors to form the cofactor matrix \(\left[\begin{matrix}3 & -12 & 6\\1 & 5 & 2\\-11 & -1 & 5\end{matrix}\right]\).
- Transpose this matrix: adj A=\(\left[\begin{matrix}3 & 1 & -11\\-12 & 5 & -1\\6 & 2 & 5\end{matrix}\right]\).
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