Using properties of determinants prove that:
\( \mathrm{P} \)
\[
\l...
Using properties of determinants prove that:
\( \mathrm{P} \)
\[
\left|\begin{array}{ccc}
3 x & -x+y & -x+z \\
x-y & 3 y & z-y \\
x-z & y-z & 3 z
\end{array}\right|=3(x+y+z)(x y+y z+z x) \text {. }
\]
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