NCERT Class 12 · Ch 4 Exercise 4.4 · Q14
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.4 Question 14
For A=\(\left[\begin{matrix}3 & 2\\1 & 1\end{matrix}\right]\), find a,b such that A²+aA+bI=0.
💡 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: a=−4, b=1.
- Compute A²=\(\left[\begin{matrix}11 & 8\\4 & 3\end{matrix}\right]\).
- The off-diagonal equation is 8+2a=0, giving a=−4. The (1,1) equation is 11+3a+b=0, giving b=1.
- Substitution gives A²−4A+I=\(\left[\begin{matrix}0 & 0\\0 & 0\end{matrix}\right]\).
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