## Differential Equations and Linear Algebra (4th Edition)

We know that the determinant of a matrix $\left[\begin{array}{rr} a & b \\ c &d \\ \end{array} \right]$ is $D=ad-bc$. Hence for the matrix a matrix $\left[\begin{array}{rr} 1 & 1 \\ 2 &1 \\ \end{array} \right]$ $D=1\cdot1-1\cdot2=1-2=-1$ whereas all the entries are positive. Thus the statement is false.