Question 85

Consider the matrices : $$A = \begin{bmatrix} 2 & -5 \\ 3 & m \end{bmatrix}, B = \begin{bmatrix} 20 \\ m \end{bmatrix}$$ and $$X = \begin{bmatrix} x \\ y \end{bmatrix}$$. Let the set of all $$m$$, for which the system of equations $$AX = B$$ has a negative solution (i.e., $$x < 0$$ and $$y < 0$$), be the interval $$(a, b)$$. Then $$8\int_a^b |A| \, dm$$ is equal to ________


Correct Answer: 450

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