`|[xp+y, x, y] , [yp+z, y, z] , [0, xp+y, yp+z]|=0` if

det [[xp + y, x, yyp + z, y, z0, xp + y, yp + z]] = 0 if

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]|

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 x y z b. 2x y z c. 3x y z d. 4x y z

If [[x-y-z] , [-y+z] , [z]] = [[0], [5] , [3]] then find the values of x, y and z

A(x, y, z)=" min. "(x+y, y+z, z+x) B(x, y, z)="max "(x-y, y-z, z-x) C(x, y, z)=" max"(A(x, y, z), B(x, y, z)) D(x, y, z)=" min "(A(x, y, z), B(x, y, z)) Whgat is the value D(1, 2, C(0, 1, 2)) ?

A(x, y, z)=" min. "(x+y, y+z, z+x) B(x, y, z)="max "(x-y, y-z, z-x) C(x, y, z)=" max"(A(x, y, z), B(x, y, z)) D(x, y, z)=" min "(A(x, y, z), B(x, y, z)) The value of D(0, 1, 2) is :

If x,y,z are in GP, then using properties,det[[px+y,x,ypy+z,y,z0,px+y,py+z]]=0 where x!=y!=z and p is any real number.