Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Linear Algebra Bilinear Forms,Quadratic Forms
For a ∈ ℝ, let \(A_a=\left(\begin{array}{ccc}2 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & a\end{array}\right)\). Which one of the following statements is true ?
1
Aa is positive definite for all a < 3.
2
Aa is positive definite for all a > 3.
3
Aa is positive definite for all a ≥ -2.
4
Aa is positive definite only for finitely many values of a.