Consider the matrices A = 2 -5 3 m, B = 20 m, and X = x y. Let th… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 6 April, Shift 1Solving Linear Equations (Matrix Method)

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:

A
$450$
B
$400$
C
$500$
D
$350$

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