The eigen vector corresponding to the smallest eigen value is
putting λ equal to 1.
Rank of the coefficient matrix=
= Number of non-zero diagonal elements
= 2 < 3.
Hence non-zero solution vector = 3 - 2 = 1
These equation can be rewritten as
From these equations,
Hence is the required eigen vector.
29. Eigen values of the system represented by
X | = |
| X | are |