Teaching CSIR NET Mock Test Series Mathematical Science Linear Algebra Bilinear Forms,Quadratic Forms
Let A be a real diagonal matrix with characteristic polynomial λ3 - 2λ2 - λ + 2. Define a bilinear form 〈v, w〉 = vt Aw on ℝ3. Which of the following statements are true?
1
A is positive definite
2
A2 is positive definite.
3
There exists a nonzero v ∈ ℝ3 such that 〈v, v) = 0.
4
rank A = 2.