Question

Suppose T€L(R^2) is defined by T(x, y) =(-3y,x).find the eigenvalues of T

Answer 1

Answer:-

 Let $\lambda$ be an eigenvalues of T such that $T(x,y)=λ(x,y)$ .

 Then we have $T(x,y)=λ(x,y)$ so $(−3y,x)=(λx,λy)$ , thus $λx=−3y$  and $x=λy$ . So we have $λ(λy)=−3y$

 implies we have $\lambda^2 = -3$ . which has no solution. So there arent any eigenvalues.