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

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

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

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

Prove that |[1+a,1, 1], [1,1+b,1], [1, 1, 1+c]|=a b c(1+1/a+1/b+1/c)=a b c+b c+c a+a b

prove without expanding, |[(a-b),1,a],[b-c,1,b],[c-a,1,c]|=|[a,1,b],[b,1,c],[c,1,a]|

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

A=[[0 , 6 , 7 ],[ -6, 0 , 8 ],[ 7, -8, 0]] , B=[[0, 1 ,1],[ 1 , 0 ,2],[ 1 ,2 ,0]] , C=[[2 ],[ -2],[ 3]] Calculate AC , B C and (A+B) C . Also, verify that (A+B) C=A C+B C

|{:(a-b,1,a),(b-c,1,b),(c-a,1,c):}|=|{:(a,1,b),(b,1,c),(c,1,a):}|

If A=[[0, 6, 7], [-6, 0, 8], [ 7,-8, 0]] , B=[[0, 1, 1],[ 1, 0, 2],[ 1, 2, 0]] , C=[[2], [-2] , [3]] Calculate AC, BC and (A + B)C . Also, verify that (A + B)C = A C + B C

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