[" प्र0-3(क) ",|x+y,y+z,z+x],[z,x,y],[1,1,1]|" का बिना विस्तार किए सिद्ध कीजिए "

Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=0 .

If |[x^3+1, x^2, x] , [y^3+1, y^2, y] , [z^3+1, z^2, z]|=0 and x, y, z are all different then prove that xyz=-1

x+y-z=1 3x+y-2z=3 x-y-z=-1

If x, y, z are different and Delta=|[x, x^2, 1+x^3],[y, y^2, 1+y^3],[z, z^2, 1+z^3]|=0 then show that 1+xyz=0

If x, y, z are different and Delta=|[x, x^2, 1+x^3],[y, y^2, 1+y^3],[z, z^2, 1+z^3]|=0 then show that 1+xyz=0

If xneynez and |[x,x^3,x^4-1],[y,y^3,y^4-1],[z,z^3,z^4-1]|=0 , then prove that : xyz(xy+yz+zx)=x+y+z

If [(x+y,x-y),(2x+z,x+z) ] =[(0,0),(1,1)] then find values of x,y and z

2x+y-z=1 x-y+z=2 3x+y-2z=-1

If x != y != z and |[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,1+z^3]]|=0 then using properties of determinants, show that xyz= -1.