Science:Math Exam Resources/Courses/MATH152/April 2022/Question B3 (b)/Hint 1

Based on the work in part (a), we are looking for vector solutions to the equations

$$Av=-v\qquad {\text{and}}\qquad Av=5v.$$

Each vector equation above is a system of three linear equations. Can you try to solve these? Which one do you expect to have a two-dimensional solution space?