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([x+y,y+z],[z,x],[1,1])=0...

([x+y,y+z],[z,x],[1,1])=0

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Show without expanding at any stage that: [x+y,y+z,z+x],[z,x,y],[1,1,1]|=0

Without expanding prove that abs[[x+y,y+z,z+x],[z,x,y],[1,1,1]]=0

Without expanding,prove that quad Delta=det[[x+y,y+z,z+xz,x,y1,1,1]]=0

Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=0 .

Without expanding prove that det[[x+y,z,1y+z,x,1z+x,y,1]]=0

If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0 , then x^(-1)+y^(-1)+z^(-1) is equal to a.1 b.-1 c.-3 d. none of these

If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0 , then x^(-1)+y^(-1)+z^(-1) is equal to a.1 b.-1 c.-3 d. none of these

If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0 , then x^(-1)+y^(-1)+z^(-1) is equal to a.1 b.-1 c.-3 d. none of these

By using properties of determinant prove that |(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0

Without expanding, prove that Delta=|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0