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Show that : |x y z x^2y^2z^2x^3y^3z^3|=x...

Show that : `|x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot`

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`|(x,y,z),(x^2,y^2,z^2),(x^3 , y^3,z^3)|`
`= xyz|(1,1,1),(x,y,z),(x^2,y^2,z^2)|`
`c_2 -> c_2 - c_1`
`c_3 -> c_3 - c_1`
`=> |(1,0,0),(x, y-x, z-x),(x^2, y^2-x^2, z^2-x^2)|`
`= 1((y-x)(z^2-x^2) - (z-x)(y^2 - x^2))`
`= xyz(y-x)(z-x)(z+x-y-x)`
`= xyz(y-x)(z-x)(z-y)`= RHS
...
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  3. Show that : |x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot

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  12. A matrix A of order 3xx3 has determinant 5. What is the value of |3A|?

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