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सिद्ध कीजिए की |{:(,1,x,y+z),(,1,y,z+x),...

सिद्ध कीजिए की `|{:(,1,x,y+z),(,1,y,z+x),(,1,z,x+y):}|=0`

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|(x,1,y+z),(y,1,z+x),(z,1,x+y)|=

|{:(x,1,y+z),(y,1,z+x),(z,1,x+y):}|=.......

Find the value of the "determinant" |{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|

Find the value of the "determinant" |{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|

Prove that : |{:(1,x,yz),(1,y,zx),(1,z,xy):}|=(x-y)(y-z)(z-x)

|[x,1,y+z],[y,1,z+x],[z,1,x+y]|=

Show that |{:(1,x, x ^(3)),(1,y,y ^(3)),(1,z,z^(3)):}| = (x-y) (y-z) (z-x) (x + y + z)

if x+y+z=0 , then show that, |{:(1,1,1),(x,y,z),(x^3,y^3,z^3):}|=0

Prove that : |{:(1,x,x^(3)),(1,y,y^(3)),(1,z,z^(3)):}| =(x-y)(y-z)(z-x)(x+y+z)

Find the value of : |(1+x,y,z),(x,1+y,z),(x,y,1+z)|