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By using properties of determinants. Sho...

By using properties of determinants. Show that:`|[x,x^2,y z],[ y, y^2,z x],[ z, z^2,x y]|=(x-y)(y-z)(z-x)(x y+y z+z x)`

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To prove that \[ | \begin{bmatrix} x & x^2 & yz \\ y & y^2 & zx \\ z & z^2 & xy \end{bmatrix} | = (x-y)(y-z)(z-x)(xy + yz + zx) \] we will use properties of determinants. ...
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