Exercise Solution 2.7
Denote the matrix c. We first find its eigenvalues. These are values λ such that
[2.68]
for some non-zero vector ν. This is possible only if the determinant of (c − λI) is zero, a condition that yields the equation
[s1]
Solutions are λ = 1 and λ = 4. Substituting these into [2.68] and solving, we obtain corresponding eigenvectors
[s2]