Find the value of `|[1,a,b+c],[1,b, c+a],[1,c,a+b]|.`

Evaluate the following: |[1,a, b c],[1,b, c a],[1,c, a b]|

The value of Delta = |(1,a,b +c),(1,b,c +a),(1,c,a +b)| , is

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

The value of |{:(1+a,b,c),(a,1+b,c),(a,b,1+c):}| is

Write the value of the determinant |[a,1,b+c], [b,1,c+a] ,[c,1,a+b]| .

If a,b,c are in G.P. then the value of |(a,b,a+b),(b,c,b+c),(a+b,b+c,0)|= (A) 1 (B) -1 (C) a+b+c (D) 0

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

By using properties of determinants. Show that: (i) |[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|=(a-b)(b-c)(c-a) (ii) |[1, 1, 1],[a, b, c],[ a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a+b+c)

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

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