one question: are you using decimal approximations of rational numbers?
Hi,
I'm trying to find an eigenvector of a matrix. I have λ = 1, so my matrix (A - λI) is
And from rows 2 and 3 I get these simultaneous equations
I eliminate to find and
Thus the eigenvector is
t=
But the actual answer is given as (-0.0088, 0.216, 1).
Thanks for any pointers.
Looks like you are having rounding errors.
When I calculate the eigenvector for the matrix you give, I'm getting different results than either of your answers.
See for instance here: {{1-0.5253, 0.8593, -0.1906},{ -0.8612, 1-0.5018, 0.1010},{ 0.1817, 0.1161, 1-0.0236}} - Wolfram|Alpha Results
The rounding errors you have are propagating more than you may like.
To answer your question: yes, your technique is right.
Note that there are more advanced methods to keep the rounding errors to a minimum.