- #1
toni07
- 25
- 0
Homework Statement
Let T: R^6 -> R^6 be the linear operator defined by the following matrix(with respect to the standard basis of R^6):
(0 0 0 0 0 1
0 0 0 0 1 0
1 0 0 0 0 0
0 0 0 1 0 0
0 1 0 0 0 0
0 0 1 0 0 0 )
a) Find the T-cyclic subspace generated by each standard basis vector.
b) Find all the minimal polynomial of T with respect to each standard basis vector.
c) Find all eigenvalues, eigenvectors, and eigenspaces of T(over R).
d) Find the minimal polynomial of T.
Homework Equations
The Attempt at a Solution
I used the definition of T-cyclic subspace of span{x, T(X), T^2(X),...} for part a, since the basis is already in the matrix, but I don't think I'm right. I don't understand how I'm supposed to find minimal polynomial with respect to basis, I tried to find the determinant of the matrix, but I don't really think that's the right way to go since the matrix contains standard basis. Please help.