|[3x,-x+y,-x+3],[x-y,2y,x-y],[x-z,y-z,3z]|

evaluate: |(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z)|

evaluate: |(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z)|

Using the properties of determinants in Exercise 1 to 6, evaluate |{:(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z):}|

Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z-x)dot

Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonzero real number, is equal to a. x y z b. 2x y z c. 3x y z d. 4x y z

Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonzero real number, is equal to a. x y z b. 2x y z c. 3x y z d. 4x y z

Show that: |[x-y-z,2x,2x],[2y,y-z-x,2y],[2z,2z,z-x-y]|=(x+y+z)^3

Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-x)

Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-x)

By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+z+2x,y],[z,z,z+x+2y]| = 2(x+y+z)^3