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

Calculate vectors $x$ and $y$ which satisfy

$\left(\begin{array}{cc}-1-{\lambda }_1& -2\\ 2& -1-{\lambda }_1\end{array}\right)x=0$

and

$\left(\begin{array}{cc}-1-{\lambda }_2& -2\\ 2& -1-{\lambda }_2\end{array}\right)y=0$

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