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        Please prove above determinants in the photo that they are equal
3 years ago

mycroft holmes
272 Points
							Given determinant can be written as the product of two determinants as:
$\begin{vmatrix} a^2 & -2a & 1\\ b^2 & -2b & 1\\ c^2 & -2c & 1 \end{vmatrix} \times \begin{vmatrix} 1 & 1 & 1\\ p & q & r\\ p^2 & q^2 & r^2 \end{vmatrix}$$= -\begin{vmatrix} a^2 & 2a & 1\\ b^2 & 2b & 1\\ c^2 & 2c & 1 \end{vmatrix} \times \begin{vmatrix} 1 & 1 & 1\\ p & q & r\\ p^2 & q^2 & r^2 \end{vmatrix}$
$= \begin{vmatrix} 1& 2a & a^2\\ 1 & 2b & b^2\\ 1 & 2c & c^2 \end{vmatrix} \times \begin{vmatrix} 1 & 1 & 1\\ p & q & r\\ p^2 & q^2 & r^2 \end{vmatrix}$
$= \begin{vmatrix} (1+ap)^2& (1+aq)^2 & (1+ar)^2\\ (1+bp)^2& (1+bq)^2 & (1+br)^2\\ (1+cp)^2& (1+cq)^2 & (1+cr)^2 \end{vmatrix}$

3 years ago
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