Toronto Math Forum
MAT2442014F => MAT244 MathLectures => Topic started by: Sheng Zang on December 07, 2014, 01:50:12 PM

I got a question like this,
As I solved, I find the critical point is (0,0) and A= (0 1)
(6x^2+8 0)
after plug(0,0) into, it becomes (0, 1)
(0, 0)
so, Î»1=0=Î»2, how to solve eigenvector and determine the type of critical point?
Thanks for help.

your post is incomprehensible
How to find eigenvector? See Linear algebra course and Sections 7.1, 7.2 of our textbook

I mean forÎ»1=0, matrix is A=(0 1) *(x1) =(0)
(0 0) (y1) (0)
the eigenvector is (1,0) which is horizontal.
and since Î» is repeated, i.e Î»1=Î»2=0,
we solve (0 1) *(x2) =(1)
(0 0) (y2) (0)
so, another eigenvector is (0,1), which is vertical.
Am I correct?

Except $(0,1)$ is not an eigenvector but a generalized e.v.

Also what is the type of critical point? proper or improper node? And how to draw pic?( I don't think this is as usual as we draw (im)proper node picture)

Improper node. See in Textbook. Forum is not a substitution for it