The matrix A 1 1 1 1 1 0 3 1 2 has one real eigenvalue Find

The matrix A [-1 -1 -1 1 -1 0 3 1 2] has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace eigenvalue= multiplicity= dimension of eigenspace=

Solution

eien value can be computed from the equation arised from det( A - xI₃) = 0

This gives us,

x + x³ = 0 whch gives us \'0\' as areal solution and i and -i as the other complex roots.

its multipliciy is 1 , So the dimension is also 1 of the eigen space