71. Let A be a *k* ** *k* symmetric matrix and define *i* by $$_1 =

71. Let A be a *k* *×* *k* symmetric matrix and define δ_*i* by

$$δ_1 = a_{11}, δ_2 =

\begin{vmatrix}

a_{11} & a_{12} \\

a_{21} & a_{22}

\end{vmatrix}, ..., δ_k = |A|.$$

Show that δ_*i* ≥ 0 for *i* = 1, 2, ..., *k* is not a sufficient condition for A to non-negative.