Recall that $A \in \operatorname{Mat}(n, \mathbb{R})$ is called nilpotent if there exists n > 0 such that $A^n = 0.$ Observe that if A is nilpotent then its characteristic polynomial is, up to a sign,$p(λ) = λ^n$ .After identifying $ \mathfrak{sl}(2, \mathbb{R})$ with $\mathbb{R}^3 $ as vector spaces, show that the set of nilpotent matrices in $ \mathfrak{sl}(2, \mathbb{R})$ is quadratic cone in $\mathbb{R}^3 $ described by the equation $x^2 +yz = 0$
I'm kind of lost in question and I just have to finish my work. What would be the set $ Mat (2, \mathbb{R} $) and the main space icon $ \mathbb {R}^3 $, the principal, which equation $ x ^ 2 + yz = 0 $ has a To see it all, if anyone can help, I'll be very grateful.
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