Find the eigenvalues and eigenvectors of the matrix A =

⎛

⎝

1 0 −4 0 5 4

−4 4 3

⎞

⎠.

Hence show that the system ˙x = Ax can be transformed into ˙u = J u, where J =

⎛

⎝

3 0 0 0 −3 0 0 0 9

⎞

⎠.

Sketch a phase portrait for the system ˙u = J u.