Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 29/Solution 1
If a vector lies in the line of rotation, after multiplying the rotational matrix on the vector, the vector stays the same.
That is to say if we denote this vector by , then we have
Equivalently we are looking for eigenvector corresponding to eigenvalue 1. We need to solve characteristic equation
By row reduction we have Thus and , i.e., So the eigenvector is which is the vector direction of axis.