Prove that `|{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}|=abc(1/a+1/b+1/c+1)`

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,1,1),(a,b,c),(a^3,b^3,c^3):}|=(a-b)(b-c)(c-a)(a+b+c)

Evaluate Delta=|{:(1,a,bc),(1,b,ca),(1,c,ab):}|

If a,b,c and d are the roots of the equation x^(4)+2x^(3)+4x^(2)+8x+16=0 the value of the determinant |{:(1+a,1,1,1),(1,1+b,1,1),(1,1,1+c,1),(1,1,1,1+d):}| is

If the value of the determinant |{:(a,1,1),(1,b,1),(1,1,c):}| is positive then

Let a,b,c be such that b(a+c) ne 0 . If |{:(,a,a+1,a-1),(,-b,b+1,b-1),(,c,c-1,c+1):}|+|{:(,a+1,b+1,c-1),(,a-1,b-1,c+1),(,(-1)^(n+2)a,(-1)^(n+1)b,(-1)^(n)c):}|=0 , Then the value of 'n' is:

Prove that: {:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0

If A,B and C are the angle of a non-right angled Delta ABC the value of |{:(tanA,1,1),(1,tanB,1),(1,1,tanC):}| is

Without expanding the determinant prove that |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

If ane0, bne0,cne0 " "and " |{:(1+a,1,1),(1+b,1+2b,1),(1+c,1+c,1+3c):}| =0 the value of |a^(-1)+b^(-1)+c^(-1)| is equal to