By using properties of determinant prove that`|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0`

Using properties of determinant show that |(1,log_x y,log_x z),(log_y x,1,log_y z),(log_z x,log_z y,1)|=0

Without expanding the determinants, show that |(1,x,x^2),(1,y,y^2),(1,z,z^2)|=(y-x)(z-y)(z-x)

Without expanding,show that the values of the following determinants are zero: |(1,4,y+z),(1,4,z+x),(1,4,x+y)|

Expand the following determinants: |(0,x,y),(-x,0,z),(-y,-z,0)|

Without expanding,show that the values of the following determinants are zero: |(1,x,x^2-yz),(1,y,y^2-zx),(1,z,z^2-xy)|

Prove that |(x+y,y+z,z+x),(z+x,x+y,y+z),(y+z,z+x,x+y)|=2|(x,y,z),(z,x,y),(y,z,x)|

Select the correct options from the given alternatives.If |(x^k,x^(k+2),x^(k+3)),(y^k,y^(k+2),y^(k+3)),(z^k,z^(k+2),z^(k+3))|=(x-y)(y-z)(z-x)(1/x+1/y+1/z) then

Find x,y,z using Cramer's Rule,if 2/(x+y)-4/(y-1)+1/(z+1)=-7,4/(x+y)+1/(y-1)-3/(z+1)=-11 ,3/(x+y)+1/(y-1)+1/(z+1)=2