|[1,a,b+c],[1,b,c+a],[1,c,a+b]|=0

Show without expanding at any stage that: [1,a,b+c],[1,b,c+a],[1,c,a+b]|=0

Prove: |(1,a, b c),(1,b ,c a),(1,c ,a b)|=|(1,a ,a^2),( 1,b,b^2),( 1,c,c^2)|

Show that det[[1,a,b_(-)c1,b,c+a1,c,a+b]]=0

If D=[[1,a,b],[1,b,c],[1,c,a]] , then [[a,b,c],[b,c,a],[1,1,1]] =

prove that det[[1,a,b+c1,b,c+a1,c,a+b]]=0

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

|[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]|=0

Using the property of determinants and without expanding , prove that: |[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b]| = 0

Without expanding the determinant prove the following. |[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]|=0

Show that |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b ,c(a+b)]|=0 .