[=0],[3" Show that "|[1,a,b+c],[1,b,c+a],[1,c,a+b]|=0]

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

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

Without expanding show that |{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

Show that |1a b_c1b c+a1c a+b|=0

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

Without expanding show that : |(a,b+c,1),(b,c+a,1),(c,a+b,1)|=0

By using properties of determinants, show that : |[1,1,1],[a,b,c],[a^3,b^3,c^3]| = (a-b)(b-c)(c-a)(a+b+c)

Using properties of determinants, show that |1 a a^2 -b c 1 b b^2 -c a 1 c c^2 -a b|=0

If |[a,a^(2),1+a^(3)],[b,b^(2),1+b^(3)],[c,c^(2),1+c^(3)]|=0" and "|[a,a^(2),1],[b,b^(2),1],[c,c^(2),1]|!=0 then show that abc =-1

prove |[1, b c, a(b+c)],[ 1, c a, b(c+a)],[ 1, a b, c(a+b)]|=0