Prove that `|[1+a,1,1],[1,1+b,1],[1,1,1+c]|` = `abc (1/a+1/b+1/c+1)`

Prove that |[1+a,1, 1], [1,1+b,1], [1, 1, 1+c]|=a b c(1+1/a+1/b+1/c)=a b c+b c+c a+a b

Show that |[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc(1+1/a+1/b+1/c)=abc+bc+ca+ab

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

If a ,b and c are all non-zero and |[1+a,1, 1],[ 1,1+b,1],[1,1,1+c]|=0, then prove that 1/a+1/b+1/c+1=0

Prove that |[1,a,a^3],[1,b,b^3],[1,c,c^3]|=(a-b)(b-c)(c-a)(a+b+c)

a^(−1) + b^(−1) + c^(−1) = 0 such that |[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]| =△ then the value of △ is

Prove that |1+a1 1 1 1 1+b1 1 1 1 1+c1 1 1 1 1+d|=a b c d(a+1/a+1/b+1/c+1/d)dot Hence find the value of the determinant if a ,b ,c , d are the roots of the equation p x^4+q x^3+r x^2+s x+t=0.

If a ,b and c are all non-zero and |(1+a,1,1),( 1,1+b,1),(1,1,1+c)|=0, then prove that 1/a+1/b+1/c+1=0

If 1 + (1)/(a) + (1)/(b) + (1)/(c) = 0 , then Delta = |(1 +a,1,1),(1,1 +b,1),(1,1,1 +c)| is equal to

If a, b and c are all different from zero and Delta = |(1 +a,1,1),(1,1 +b,1),(1,1,1 +c)| = 0 , then the value of (1)/(a) + (1)/(b) + (1)/(c) is