If the value of the determinant a h g h b f g f c is abc-2x-af2-bg2-ch2 -then what is the value of -x- -

a amp; h amp; g h amp; b amp; f g amp; f amp; c =a(bc f^2) h(hc gf)+g(hf gb) =abc af^2 ch^2+gfh+ghf bg^2 =abc+ ...

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Byju's Answer

Standard XII

Mathematics

Definition of a Determinant

If the value ...

Question

If the value of the determinant $∣ ∣ ∣ ∣ \begin{matrix} a & h & g h & b & f g & f & c \end{matrix} ∣ ∣ ∣ ∣$ is $(a b c + 2 x - a f^{2} - b g^{2} - c h^{2})$ ,then what is the value of $^{'} x^{'}$ ?

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Solution

$∣ ∣ ∣ ∣ \begin{matrix} a & h & g h & b & f g & f & c \end{matrix} ∣ ∣ ∣ ∣$

$= a (b c - f^{2}) - h (h c - g f) + g (h f - g b)$

$= a b c - a f^{2} - c h^{2} + g f h + g h f - b g^{2}$

$= a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2}$
Comparing with, $(a b c + 2 x - a f^{2} - b g^{2} - c h^{2})$
we get, $x = (f g h)$

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If the value of the determinant ∣∣ ∣∣ahghbfgfc∣∣ ∣∣ is (abc+2x−af2−bg2−ch2) ,then what is the value of ′x′ ?

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If the value of the determinant $∣ ∣ ∣ ∣ \begin{matrix} a & h & g h & b & f g & f & c \end{matrix} ∣ ∣ ∣ ∣$ is $(a b c + 2 x - a f^{2} - b g^{2} - c h^{2})$ ,then what is the value of $^{'} x^{'}$ ?