The characteristic polynomial of the matrix =⎡⎣⎢⎢⎢⎢0−1000−100−43−33−32−22⎤⎦⎥⎥⎥⎥A=[00−4−3−1−13200−3−20032]
is p()=p(λ)= (+1)22(λ+1)2λ2
The matrix has two real eigenvalues 1<2λ1<λ2.
(a) Find these eigenvalues, their algebraic multiplicities (AM) , and dimensions of the corresponding eigenspaces (GM).
1=λ1= has algebraic multiplicity (AM) 2 . The dimension of the corresponding eigenspace (GM) is 2 .
2=λ2= 0 has algebraic multiplicity (AM) 2 . The dimension of the corresponding eigenspace (GM) is 1 .
(b) Is the matrix A defective?