Read Eigenvalues and Eigenvectors Invariant Directions befo

Read \'Eigenvalues and Eigenvectors -- Invariant Directions\' before attempting this problem. The linear transformation L: R^2 rightarrow R^2 maps the vector u to L(u) and the vector v to L(v). The vectors u, v, L(u), and L(v) are shown below; u and v in red and L(u) and L(v) in blue. Which of the following could be an eigenvector of L? Select all that apply. v 2u + v u + v v - u u u - 3v -u - v u - v None of the above

Solution

C. u+v

Eigenvector is something so that Lv=kv ie L acts on v and gives out a vector in same direction as v

Now note the position of Lu and Lv.

Lu+Lv will point about 45 degrees above u which is where you could expect u+v to point also.