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in Determinants by (15.2k points)

Using properties of determinants prove that:

\(\begin{bmatrix} x & y & z \\[0.3em] x^2& y^2 & z^2 \\[0.3em] x^3 & y^3 & z^2 \end{bmatrix}\)= xyz (x-y)(y-z)(z-x).

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1 Answer

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by (15.7k points)

\(\begin{bmatrix} x & y & z \\[0.3em] x^2& y^2 & z^2 \\[0.3em] x^3 & y^3 & z^2 \end{bmatrix}\)

= xyz(x - y)(y - z)(0 + 0 + y + z - x - y) [expansion by first row] 

= xyz(x - y)(y - z)( z - x)

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