Answer
See below
Work Step by Step
An example of a $2 \times 1$ matrix function $A$ that is nonconstant such that
all elements of $A(t)$ are positive for all $t$ in $R$ could be:
$−2 \leq t \lt 3$ could be:
$\begin{bmatrix}
0\\\frac{1}{t^2+1}
\end{bmatrix}$
