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

Evaluate Delta=|1a b c1b c a1c a b|

By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)

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

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

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

Using properties of determinant show that: |[1 , a , bc] , [1 , b , ca] , [1 , c , a b]|=(a-b)(b-c)(c-a)

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

If (b+c)/a,(c+a)/b,(a+b)/c are in A.P. show that 1/a,1/b1/c are also in A.P. (a +b+c != 0) .

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

If a=-10,b=1 and c=1 , Show that a -: (b+c) != (a -:b) + (a-:c)