Class 12 Determinants · Short Answer2 Marksdeterminant_equations
Class 12 Maths · Determinants · Short Answer #48
For A=\(\begin{bmatrix}2 & λ & -3\\0 & 2 & 5\\1 & 1 & 3\end{bmatrix}\), find all real λ for which A⁻¹ exists.
✅ Step-by-Step Solution
Final Answer: λ≠−8/5
- An inverse exists precisely when det(A)≠0.
- Expansion gives det(A)=2(6−5)−λ(0−5)−3(0−2)=8+5λ.
- Thus 8+5λ≠0, so λ≠−8/5.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] An inverse exists precisely when det(A)≠0.
- [1 mark] Expansion gives det(A)=2(6−5)−λ(0−5)−3(0−2)=8+5λ.
- [0.5 marks] Thus 8+5λ≠0, so λ≠−8/5.
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