15. Probs. 15, 16, 17, and 18 will illustrate Theorem 11.3.3. Define the Z-matrices A and B by (note A ≤ B)

$$A = \begin{bmatrix} 2 & -1 & 0 \\ -1 & 2 & 0 \\ -2 & -1 & 1 \end{bmatrix}; B = \begin{bmatrix} 3 & -1 & 0 \\ 0 & 2 & 0 \\ -1 & -1 & 1 \end{bmatrix}$$

Show that each real characteristic of A is positive.