Let A be a square matrix of order 2 such that |A|=2 and the sum of its diagonal elements i…

Question

Let $A$ be a square matrix of order 2 such that $|A|=2$ and the sum of its diagonal elements is -3 . If the points $(x, y)$ satisfying $$\mathrm{A}^2+x \mathrm{~A}+y \mathrm{I}=\mathrm{O}$$ lie on a hyperbola, whose transverse axi...

Answer: 25

Accepted Answer

$|A|=2\sum dia=-3$

$	herefore \,$ character equation : ${A}^{2}+3A+2I=0$

$\Rightarrow x=3\, y=2$

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

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

$	herefore $ multiple value of '$e$' and $L(LR)$ is possible.

We'll not get a unique result.

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