Teaching DSSSB TGT Mock Test 2025 Mathematical Science Linear Algebra Bilinear Forms,Quadratic Forms
Let (-, -) be a symmetric bilinear form on ℝ2 such that there exist nonzero v, w ∈ ℝ2 such that (v, v) > 0 > (w, w) and (v, w) = 0. Let A be the 2 × 2 real symmetric matrix representing this bilinear form with respect to the standard basis. Which one of the following statements is true?
1
A2 = 0.
2
rank A = 1.
3
rank A = 0.
4
there exists u ∈ ℝ2, u ≠ 0 such that (u, u) = 0.