Let Delta = begin{vmatrix} Ax & x^2 & 1 By | vedclass

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(B) Given $ \Delta = \begin{vmatrix} Ax & x^2 & 1 \ By & y^2 & 1 \ Cz & z^2 & 1 \end{vmatrix} $. Taking $ x, y, z $ common from $ R_1, R_2, R_3 $ re

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$ \Delta_1 = \Delta $

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(B) Given $ \Delta = \begin{vmatrix} Ax & x^2 & 1 \ By & y^2 & 1 \ Cz & z^2 & 1 \end{vmatrix} $. Taking $ x, y, z $ common from $ R_1, R_2, R_3 $ respectively: $ \Delta = xyz \begin{vmatrix} A & x & \frac{1}{x} \ B & y & \frac{1}{y} \ C & z & \frac{1}{z} \end{vmatrix} $. Multiply $ C_3 $ by $ xyz $: $ \Delta = \begin{vmatrix} A & x & yz \ B & y & zx \ C & z & xy \end{vmatrix} $. Taking the transpose of the determinant (rows become columns): $ \Delta = \begin{vmatrix} A & B & C \ x & y & z \ yz & zx & xy \end{vmatrix} = \Delta_1 $. Thus,$ \Delta_1 = \Delta $.

Let $ \Delta = \begin{vmatrix} Ax & x^2 & 1 \\ By & y^2 & 1 \\ Cz & z^2 & 1 \end{vmatrix} $ and $ \Delta_1 = \begin{vmatrix} A & B & C \\ x & y & z \\ zy & zx & xy \end{vmatrix} $,then:

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