1. The problem statement, all variables and given/known data Let A be the matrix of the linear transformation T. Without writing A, find an eigenvalue of A and describe the eigenspace. T is the transformation on R^3 that rotates points about some line through the origin. 2. Relevant equations maybe...Ax=(lambda)x ? 3. The attempt at a solution The biggest issue for me is imagining this problem geometrically. I am not sure if I understand it. Any eigenvector will be on this line through the origin that, despite the transformation, remains on that line. So any eigenvalue corresponding to that eigenvector is valid? (and given the abstract question, can I answer it as such? thats also somewhat new and strange to me.) As for the description of the eigenspace, which is the null space of the matrix A-(lambda)I would that just be a single vector with three entries? I think this because the generation of a line in R^3 is done with the linear combinations of a single vector. I am imagining that when the question says " rotates points about some line through the origin" the points on the line stay in place, while points outside the line in three space are rotated around this line. My problem with this class in general, I think, is making the jump from primarily computational problems with some theory mixed in, to primarily theoretical problems, with computational mixed in. I usually enjoy these types of problems, but I think im having an off semester or something. Thanks for your time.