Part BCSIR NET December 2023indefinite-implies-isotropic

Indefinite implies isotropic

Let (−, −) be a symmetric bilinear form on $R^{2}$ such that there exist nonzero $v, w \in R^{2}$ with (v, v) > 0 > (w, w) and (v, w) = 0. Let A be the 2×2 real symmetric matrix representing this form in the standard basis. Which one of the following statements is true?

A. $A^{2} = 0$ .
B.rank A = 1.
C.rank A = 0.
D.There exists $u \in R^{2}, u \neq = 0$ such that (u, u) = 0.

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Converse assumed

The theorem runs one way. You used it in the other.

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Indefinite implies isotropic

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