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Prove that |{:(1, " "1, " "1), (1, 1+x, ...

Prove that `|{:(1, " "1, " "1), (1, 1+x, " "1), (1, " "1, 1+y):}|=xy.`

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Prove that: |(1, 1, 1),( 1, 1+x,1) ,(1, 1, 1+y)|=x y .

Using properties of determinants prove that |(1,1, 1+3x),(1+3y,1,1),(1, 1+3z,1)| =9(3xyz+xy+yz+zx)

|{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=xy+yz+zx+xyz

Using prperties of determinants, prove that : |(1,1,1+3x),(1+3y,1,1),(1,1+3z,1)| = 9(3xyz + xy + yz + zx) .

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

|(1+x,1,1),(1,1+y,1),(1,1,1+z)|=xy+yz+zx+xyz

Value of the determinant |(x,1,1),(0,1+x, 1),(-y, 1+x, 1+y)| is (A) xy (B) xy(x+2) (C) x(x+1)(y+1) (D) xy(x+1)

Value of the determinant |(x,1,1),(0,1+x, 1),(-y, 1+x, 1+y)| is (A) xy (B) xy(x+2) (C) x(x+1)(y+1) (D) xy(x+1)

Using properties of determinants prove that ((1,1,1+3x),(1+3y,1,1),(1,1+3z,1)=9(3xyz+xy+yz+zx)