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

Select and write the correct answer from the given alternatives in each of the following:The determinant |(xp+y,x,y),(yp+z,y,z),(0,xp+y,yp+z)|=0 for all p in R if

Without expanding,show that the values of the following determinants are zero: |(x,y,z),(x+3a,y+3b,z+3c),(a,b,c)|

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

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)|

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

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

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

Solve the following: Show the matrix [[x+y,y+z,z+x],[1,1,1],[z,x,y]] is a singular