Given `Delta=|(y+z,x,y),(z+x,z,x),(x+y,y,z)|` Perform `C_1rarrC_1-2C_3`,`C_2rarrC_2-C_3`

Given Delta=|(y+z,x,y),(z+x,z,x),(x+y,y,z)| Apply R_1rarrR_1+R_2+R_3 .

Given Delta=|(y+z,x,y),(z+x,z,x),(x+y,y,z)| Take (x+y+z) common from R_1 .

Given Delta=|(y+z,x,y),(z+x,z,x),(x+y,y,z)| Prove that Delta=(x+y+z)(x-z)^2 .

Given Delta=|(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3)| Prove that Delta=(1+pxyz)(x-y)(y-z)(z-x) .

Delta_(1) = |(y^(5)z^(6) (z^(3)-y^(3)),x^(4)z^(6)(x^(3)-z^(3)),x^(4)y^(5)(y^(3)-x^(3))),(y^(2)z^(3)(y^(6)-z^(6)),xz^(3)(z^(6)-x^(6)),xy^(2)(x^(6)-y^(6))),(y^(2)z^(3)(z^(3)-y^(3)),xz^(3)(x^(3)-z^(3)),xy^(2)(y^(3)-x^(3)))| and Delta_(2)=|(x,y^(2),z^(3)),(x^(4),y^(5),z^(6)),(x^(7), y^(8),z^(9))| Then Delta_(1) Delta_(2) is equal to a) Delta_(2)^(2) b) Delta_(2)^(3) c) Delta_(2)^(4) d)None of these

Value of |(x+y,z,z),(x,y+z,x),(y,y,z+x)| where x , y ,z are non - zero real number is equal to a)xyz b)2xyz c)3xyz d)4xyz

Given Delta=|(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3)| Express this as sum of two determinants.

Prove that |(1,x,x^3),(1,y,y^3),(1,z,z^3)|=(x+y+z)(x-y)(y-z)(z-y) .

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

Given a = x/(y - z), b = y/(z - x) and c = z/(x - y) , where x,y and z are not all zero, Then the value of ab + bc + ca a)0 b)1 c)-1 d)None of these