Let V = "

v1 v2 #

denote a matrix formed from the eigenvectors. Thus, if v1 =

 1

−2



and v2 =



1 2



then V =

 1 1

−2 2 

The determinant of this matrix is called the Wronksian, i.e., W(v1, v2) =

det(V). Then v1 and v2 are linearly independent if and only if W(v1, v2)

is nonzero.

Show that for the system x˙ = x + y y˙ = −2x + 4y the Wronksian is nonzero.