|[1,ab,(1)/(a)+(-)/(b)],[1,bc,(1)/(b)+(1)/(c)],[1,ca,(1)/(c)+(1)/(a)]

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

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

|[(1)/(a),a^(2),bc],[(1)/(b),b^(2),ca],[(1)/(c),c^(2),ab]|=0

(1)/(a),a^(2),bc(1)/(b),b^(2),ca(1)/(c),c^(2),ab]|

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

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

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