" Without expansion,evaluate "|[1,ab,(1)/(a)+(1)/(b)],[1,bc,(1)/(b)+(1)/(c)],[1,ca,(1)/(c)+(1)/(a)]|

Prove that |{:(1,,ab,,(1)/(a)+(1)/(b)),(1 ,,bc,,(1)/(b)+(1)/(c)),( 1,, ca,,(1)/(c)+(1)/(a)):}|=0

Prove that |{:(1,,ab,,(1)/(a)+(1)/(b)),(1 ,,bc,,(1)/(b)+(1)/(c)),( 1,, ca,,(1)/(c)+(1)/(a)):}|=0

Prove that |{:(1,,ab,,(1)/(a)+(1)/(b)),(1 ,,bc,,(1)/(b)+(1)/(c)),( 1,, ca,,(1)/(c)+(1)/(a)):}|=0

If a,b,c are non-zero real numbers, then |(1,ab,(1)/(a)+(1)/(b)),(1,bc,(1)/(b)+(1)/(c)),(1,ca,(1)/(c)+(1)/(a))| is a)0 b)bc+ca+ab c) a^(-1)+b^(-1)+c^(-1) d)None of these

Without expanding prove that , |{:(1,ab,1/a+1/b),(1,bc,1/b+1/c),(1,ca,1/c+1/a):}|=0

Evaluate: |[1,a,bc],[1,b,ca],[1,c,ab]|

Without expanding prove that, abs((1,ab,1/a+1/b),(1,bc,1/b+1/c),(1,ca,1/c+1/a)) = 0

Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(2),-ab]|=0

Without expanding at any state, prove that |((1)/(a),a,bc),((1)/(b),b,ca),((1)/(c ),c,ab)|=0

|[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]|=0