Delta=|[0,b-a,c-a],[a-b,0,c-b],[a-c,b-c,0]|

If Delta=det[[0,b-a,c-aa-b,0,c-ba-c,b-c,0]], then Delta

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

Without expanding or evaluating show that |(0,b-a, c-a),( a-b,0,c-b),( a-c ,b-c,0)|=0 .

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

If a, b, c are complex numbers, then the determinant Delta = |(0,-b,-c),(bar(b),0,-a),(bar(c),bar(a),0)| , is

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