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[" 1.Without expanding the determinants,...

[" 1.Without expanding the determinants,prove that "],[qquad |[ax,by,cz],[x^(2),y^(2),z^(2)],[1,1,1]|=|[a,v,c],[x,y,z],[yz,zx,xy]|]

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Prove that: |[ax,by,cz], [x^2,y^2,z^2], [1,1,1]| = |[a,b,c],[x,y,z],[yz,zx,yx]|

Without expanding the determinant , prove that |{:(ax,by,cz),(x^2,y^2,z^2),(1,1,1):}|=|{:(a,b,c),(x,y,z),(yz,zx,xy):}|

|[1/x,1/y,1/z],[x^(2),y^(2),z^(2)],[yz,zx,xy]|

Prove that |{:(ax,,by,,cz),(x^(2),,y^(2),,z^(2)),(1,,1,,1):}|=|{:(a,,c,,c),(x,,y,,z),(yz,,xz,,xy):}|

Prove that |{:(ax,,by,,cz),(x^(2),,y^(2),,z^(2)),(1,,1,,1):}|=|{:(a,,c,,c),(x,,y,,z),(yz,,xz,,xy):}|

Prove that |{:(ax,,by,,cz),(x^(2),,y^(2),,z^(2)),(1,,1,,1):}|=|{:(a,,b,,c),(x,,y,,z),(yz,,xz,,xy):}|

Prove that |{:(ax,,by,,cz),(x^(2),,y^(2),,z^(2)),(1,,1,,1):}|=|{:(a,,b,,c),(x,,y,,z),(yz,,xz,,xy):}|

proof |[x,y,z],[x^(2),y^(2),z^(2)],[yz,zx,xy]| = |[1,1,1],[x^(2),y^(2),z^(2)],[x^(3),y^(3),z^(3)]|

" (d) "|[x,y,z],[x^(2),y^(2),z^(3)],[yz,zx,xy]|=|[1,1,1],[x^(3),y^(2),z^(2)],[x^(3),y^(3),z^(3)]|