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|[x+y+z,-z,-y],[-z,x+y+z,-x],[-y,-x,x+y+...

|[x+y+z,-z,-y],[-z,x+y+z,-x],[-y,-x,x+y+z]|=2(x+y)(y+z)(z+x)

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show that |[y+z ,x, y],[ z+x, z, x],[x+y, y ,z]|=(x+y+z)(x-z)^2

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

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

By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|=2(x+y+z)^3

y+z,x,yz+y,z,xx+y,y,z]|=(x+y+z)(x-z)^(2)

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)

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

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

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