I'm a student at UNC Chapel Hill in the Honors college and I think I could be a reasonably decent physicist. Physics in general interests me enough that I spent free time reading about it, particularly astrophysics. However, I'm also quite interested in finance and computer science, so I'm a bit...
Provided that all the eigenvectors of A are zero vectors save for one of them which has only one nonzero entry, wouldn't that suggest that the eigenspace of A is only 1 dimensional? So, in order for A to be diagonalizable, the eigenspace would have to be of dimension 5, but it is of dimension 1...
So I've found all eigenvalues to be equal to 2, the first eigenvector i think is:
[1]
[0]
[0]
[0]
[0]
and the other four all all 5x1 zero vectors.
But what does that mean in the context of the question?
Homework Statement
Determine if this matrix is diagonalizable and explain why or why not.
[ 2 1 0 0 0 ]
[ 0 2 1 0 0 ]
[ 0 0 2 1 0 ]
[ 0 0 0 2 1 ]
[ 0 0 0 0 2 ]
Homework Equations
No equations provided and the use of a calculator will be prohibited on the test, so that's...