Show that `|[b-c,c-a, a-b],[ c-a, a-b,b-c],[ a-b,b-c,c-a]|` = 0 .

Show that abs{:(b-c,c-a,a-b),(c-a,a-b,b-c),(a-b,b-c,c-a):}=0.

show that det[[a-b,b-c,c-ab-c,c-a,a-bc-a,a-b,b-c]]=0

Show that |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

If a, b and c are real numbers, and triangle = |[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]| = 0 Show that either a+b+c = 0 or a=b=c

Without expanding or evaluating show that |[0 , b-a , c-a] , [a-b , 0 , c-b] , [a-c , b-c , 0]|=0

Show that: |[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]| = (a+b+c)(a^2+b^2+c^2)dot

Show that det[[0,b-a,c-aa-b,0,c-ba-c,b-c,0]]=0

If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]|=0 . Show that either a+b+c=0 or a=b=c

If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]|=0 . Show that either a+b+c=0 or a=b=c

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