\b[False.] Every entry of $A=\begin{pmatrix}1&2\\2&1\end{pmatrix}$ is strictly positive, yet $A(1,-1)^T=-(1,-1)^T$. Its <eigenvalues> are $3$ and $-1$, so one has negative real part. Positivity of entries does not imply the <positive-definite matrix> property.

Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / ib / Paper 1 / 1E / iii / Solution

 Solution (source code)