दर्शाइये कि `|{:(a+x,y,z),(a,a+y,z),(x,y,a+z):}|=a^(2)(a+x+y+z)`

|{:(a+x," "y," "z),(" "x,a+y," "z),(" "x," "y,a+z):}|=a^2(a+x+y+z)

The value of |(x+y,y+z,z+x),(x,y,z),(x-y,y-z,z-x)|=

Using properties of determinants, prove that |{:(x,y,z),(x^(2),y^(2),z^(2)),(y+z,z+x,x+y):}|=(x-y)(y-z)(z-x)(x+y+z)

Prove that : |{:(y+z,x,y),(z+x,z,x),(x+y,y,z):}|=(x+y+z)(x-z)^(2)

Prove that : |{:(y+z,x,y),(z+x,z,x),(x+y,y,z):}|=(x+y+z)(x-z)^(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)) 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)) What is the value of A(2, 3, 4)+B(2, 3, 4) ?

Prove that : |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,x+z+2y):}|=2(x+y+z)^(3)

Prove that: {:|(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=|(x,x^2,x^3),(y,y^2,y^3),(z,z^2,z^3)| = xyz(x-y(y-z)(z-x)

Prove the following : |{:(x,y,z),(x^(2),y^(2),z^(2)),(x^(3),y^(3),z^(3)):}|=|{:(x,x^(2),x^(3)),(y,y^(2),y^(3)),(z,z^(2),z^(3)):}|=xyz(x-y)(y-z)(z-x)