" 12."|[x,x^(2),1+px^(3)],[y,y^(2),1+py^(3)],[z,z^(2),1+pz^(3)]|=(1+pxyz)(x-y)(y-z)(z-x)," where "p" is any scal "

Using properties of determinants.Prove that |xx^(2)1+px^(3)yy^(2)1+py^(3)zz^(2)1+pz^(3)|=(1+pxyz)(x-y)(y-z)(z-x) where p is any scalar.

{:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(3)),( z,z^(2) , 1+pz^(3)) ]:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

{:|( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) |:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

using properties of determinant prove that {:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) ]:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

Prove that [[x, x^2 , 1+px^3], [y, y^2, 1+py^3] ,[z, z^2, 1+pz^3]] = (1+pxyz)(x-y)(y-z)(z-x)

Using properties of determinants, prove the following: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]|=(1+pxyz)(x-y)(y-z)(z-x)

Using properties of determinants, prove the following: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]|=(1+pxyz)(x-y)(y-z)(z-x)

Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]| = (1+pxyz)(x-y)(y-z)(z-x)