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QJEEM24Ma8303: JEE Main 2024 Mathematics - Class 12 JEEM24Ma8303 Solution: Let be a square matrix of order 2 such that and the sum of its…

Let AA be a square matrix of order 2 such that ∣A∣=2|A|=2 and the sum of its diagonal elements is −- 3 . If the points (x,y)(x, y) satisfying A2+x A+yI=O\mathrm{A}^2+x \mathrm{~A}+y \mathrm{I}=\mathrm{O} lie on a hyperbola, whose transverse axis is parallel to the xx -axis, eccentricity is e\mathrm{e} and the length of the latus rectum is ll , then e4+l4\mathrm{e}^4+l^4 is equal to ________.

Step-by-Step Verified Solution

∣A∣=2∑dia=−3|A|=2 \sum \mathrm{dia}=-3

∴\therefore \quad character equation : A2+3A+2I=0A^2+3 A+2 I=0

⇒x=3y=2\Rightarrow x=3 \quad y=2

∵\because We are getting only one point (3,2)(3,2) but its given many points satisfy this equation.

Moreover hyperbola whose transverse axis is xx axis and passing through (3,2)(3,2) is not unique.

∴\therefore multiple value of ' ee ' and L(LR)L(L R) is possible.

We'll not get a unique result.

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