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)|`

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

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

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

Select and write the correct answer from the given alternatives in each of the following:The value of |(x+y,z,z),(x,y+z,x),(y,y,z+x)| is

The solutiion of (x,y,z) the equation [(-1,0,1),(-1,1,0),(0,-1,1)][(x),(y),(z)]=[(1),(1),(2)] is (x,y,z)

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