Chapter 6.8, Problem 9E

a

To determine

To show: $\lambda$ is an eigenvalue of “A” with eigenvector $\overline{x}={\left(x_1,\mathrm{.....}{x}_k,0,\mathrm{....},0\right)}^T$

(b)

To determine

To show: the multiplicity of “r” is at most $2$ and that “r” has a nonnegative eigenvector is to be shown.

c

To determine

To calculate: the eigenvalue “r” has multiplicity $2$ and a positive eigenvector is to be shown.