[1.x-y+z=2],[2x-y=0],[2y-z=1],[2y-2x+y+z=2]

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

x-y+z=1 2x+y-z=2 x-2y-z=4

2x+y+z=1x-y+2z=-1,3x+2y-z=4

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

If |y z-x^2z x-y^2x y-z^2x z-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|=|r^2u^2u^2u^2r^2u^2u^2u^2r^2| , then r^2=x+y+z b. r^2=x^2+y^2+z^2 cdotu^2=y z+z x+x y d. u^2=x y z

Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x, y, z],[ x^2,y^2,z^2],[x^4,y^4,z^4]|=|[x^2,y^2,z^2],[x^4,y^4,z^4],[x, y, z]| =x y z (x-y)(y-z)(z-x)(x+y+z)

Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x, y, z],[ x^2,y^2,z^2],[x^4,y^4,z^4]|=|[x^2,y^2,z^2],[x^4,y^4,z^4],[x, y, z]| =x y z (x-y)(y-z)(z-x)(x+y+z)

Prove that Det [[x + y + 2z, x, y], [z, y + z + 2x, y], [z, x, z + x + 2y]] = 2 (x + y + z) ^ 3

If Delta=|{:(,x,2y-z,-z),(,y,2x-z,-z),(,y,2y-z,2x-2y-z):}| ,then