[[1,a,bc],[1,b,ca],[1,c,ab]]

Evaluate the following: |[1,1,bc],[1,b,ca],[1,c,ab]|

Delta=det[[1,a,bc1,b,ca1,c,ab]]

Answer the following: What is the value of [[1/a,1,bc],[1/b,1,ca],[1/c,1,ab]]

Using properties of determinant show that: det[[1,a,-bc1,b,-ca1,c,-ab]]=(a-b)(b-c)(c-a)det[[1,b,-ca1,c,-ab]]=(a-b)(b-c)(c-a)

Show without expanding at any stage that: [1/a, a,bc],[1/b,b,ca],[1/c, c, ab]|=0

Without expanding show that |[1/a,1,bc],[1/b,1,ca],[1/c,1,ab]|=0

|[1,1,1],[a,b,c],[bc,ca,ab]|=(a-b)(b-c)(c-a)

If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]| , B=|[1,bc, a],[1,ca, b],[1,ab, c]| , then

|[1,a^(2),bc],[1,b^(2),ca],[1,c^(2),ab]|

Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]] =0