Find the value of the determinant 1-z 1-z -x-y-z2 -y-z-x2 1-x 1-x -yy-z-x2z x-2y-z-xy -yx-y-xz2

The correct option is D 0 nbsp;D=1/x^4z^4z amp; z amp; (x+y) nbsp; (y+z) amp; x amp; x nbsp; yz(y+z) amp; xz(x+2y+z) amp; ...

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Modulus of a Complex Number

Find the valu...

Question

Find the value of the determinant $∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{1}{z} & \frac{1}{z} & - \frac{(x + y)}{z^{2}} - \frac{(y + z)}{x^{2}} & \frac{1}{x} & \frac{1}{x} - \frac{y (y + z)}{x^{2} z} & \frac{x + 2 y + z}{x y} & - \frac{y (x + y)}{x z^{2}} \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣$

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∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{1}{z} & \frac{1}{z} & - \frac{(x + y)}{z^{2}} - \frac{(y + z)}{x^{2}} & \frac{1}{x} & \frac{1}{x} - \frac{y (y + z)}{x^{2} z} & \frac{x + 2 y + z}{x z} & - \frac{y (x + y)}{x z^{2}} \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣

Δ = ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{1}{z} & \frac{1}{z} & \frac{- (x + y)}{z^{2}} \frac{- (y + z)}{x^{2}} & \frac{1}{x} & \frac{1}{x} \frac{- y (y + z)}{x^{2} z} & \frac{(x + 2 y + z)}{x z} & \frac{- (x + y)}{x z^{2}} \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣

x, y, z

(x + y) (y + z) (z + x) (\frac{1}{x} + \frac{1}{y}) (\frac{1}{y} + \frac{1}{z}) (\frac{1}{z} + \frac{1}{x})

x + y + z = x y z

x (1 - y^{2}) (1 - z^{2}) + y (1 - z^{2}) (1 - x^{2}) + z (1 - x^{2}) (1 - y^{2})

x, y, z

(x + y) (y + z) (z + x) (\frac{1}{x} + \frac{1}{y}) (\frac{1}{y} + \frac{1}{z}) (\frac{1}{z} + \frac{1}{x})

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