4. For the matrices below, determine whether each is positive definite, positive semidefinite, or neither. Use 1

(a) and 1

(b) of Theorem 12.2.2.

$$A = \begin{bmatrix} 1 & 2 & -1 \\ 2 & 4 & -2 \\ -1 & -2 & 8 \end{bmatrix}; \qquad B = \begin{bmatrix} 2 & 1 & 1 \\ 1 & 1 & -1 \\ 1 & -1 & 5 \end{bmatrix}; \qquad C = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 5 & 2 \\ 3 & 2 & 24 \end{bmatrix}$$