The determinant Nbegin vmatrix x - y - 1 x- 1 - y- 1 - 1 x- 2 - y- 2 - 1lendvmatrix -0 represents

Determinant : x amp; y amp; 1 x_1 amp; y_1 amp; 1 x_2 amp; y_2 amp; 1 =0 ∴ x(y_1 y_2) y(x_1 x_2)+1(x_1y_2 y_1x_2)=0 ∴ (y_1 y_2)x (x_1 x_2)y+ ...

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Equation of a Line Passing through 2 Points

The determina...

Question

The determinant $∣ ∣ ∣ ∣ \begin{matrix} x & y & 1 x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 \end{matrix} ∣ ∣ ∣ ∣ = 0$ represents

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The product of all the factors of determinant

$∣ ∣ ∣ ∣ ∣ \begin{matrix} x & y & 1 x^{2} & y^{2} & 1 x^{3} & y^{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$ is:

∣ ∣ ∣ ∣ ∣ \begin{matrix} (x + y)^{2} & z x & z y z x & (z + y)^{2} & x y z y & x y & (z + x)^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = 2 x y z (x + y + z)^{3}

y = s e c^{- 1} (\frac{x + 1}{x - 1}) + \sin^{- 1} (\frac{x - 1}{x + 1}), x > 0 . Find \frac{d y}{d x}

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