Have you tried just using the DEFINITIONS?
An eigenvector, v, of A with eigenvalue 2 must satisfy Ax= 2x so
which gives the equations -3x= 2x, 2y+ z= 2y, 2z= 2z, 2u= 2u. What do you get when you try to solve those equations?
| -3 , 0 , 0, 0 |
| 0 , 2, 1 , 0| = A
| 0 , 0, 2, 0 |
| 0 , 0 , 0 , 2|
The characteristic polynomial of A is (t + 3)(t − 2)^3. Find a basis for the eigenspace of A corresponding to the
eigenvalue λ = 2.
The answer is
{[0,1,0,0]^T, [0,0,0,1]^T}
Any help would be appreciated.
Have you tried just using the DEFINITIONS?
An eigenvector, v, of A with eigenvalue 2 must satisfy Ax= 2x so
which gives the equations -3x= 2x, 2y+ z= 2y, 2z= 2z, 2u= 2u. What do you get when you try to solve those equations?