Science:Math Exam Resources/Courses/MATH152/April 2012/Question 08 (b)/Hint 2

Calculate vectors $\displaystyle x$ and $\displaystyle y$ which satisfy

${\begin{pmatrix}-1-\lambda _{1}&-2\\2&-1-\lambda _{1}\end{pmatrix}}x=0$

and

${\begin{pmatrix}-1-\lambda _{2}&-2\\2&-1-\lambda _{2}\end{pmatrix}}y=0$

These correspond to the two eigenvalues from part (a).