Answer to Question #203166 in Linear Algebra for sabelo Zwelakhe Xu

Question

Suppose T 2 L(R2) is deÖned by T(x; y) = ((3y; x). Find the eigenvalues of T

Answer 1

Let 𝜆 be an eigenvalue of 𝑇. It means that $T(x,y)=\lambda(x,y)$

$(3y,x)=\lambda (x,y)$

$x=\lambda y$ and $3y=\lambda x=\lambda ^2y$

We obtain $\lambda ^2=3,\ \ \ \ \lambda =\pm \sqrt{3}$

Answer: $\lambda=\pm \sqrt{3}$ .