Consider the matrices: A= [2, -5; 3, m], B= [20; m] and X= [x; y]. Let the set of all m, for which the system of equations A X=B has a negative…

Consider the matrices : $\displaystyle A=\left[\begin{array}{cc}2 & -5 \\ 3 & m\end{array}\right], B=\left[\begin{array}{c}20 \\ m\end{array}\right]$ and $\displaystyle X=\left[\begin{array}{l}x \\ y\end{array}\right]$. Let the set of all $\displaystyle m$, for which the system of equations $\displaystyle A X=B$ has a negative solution (i.e., $\displaystyle x<0$ and $\displaystyle y<0$ ), be the interval $\displaystyle (a, b)$. Then $\displaystyle 8 \int_a^b|A| d m$ is equal to $\displaystyle \_\_\_\_$.